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Particle Physics of the early Universe

Alexey BoyarskySpring semester 2014

Early Universe

EARLY UNIVERSE

Alexey Boyarsky PPEU 1

Thermal history of the Universe

Today you all got used to pictures like this


History

HOW DID WE LEARN ALL THAT?


Cosmological model of Einstein

Einstein applys GR to the whole Universe assuming spatial 1917 – early1920shomogeneity and isotropy (for isotropy there were observational evidence, for

homogeneity — it was a bold extrapolation, due to Hubble’s observations of fainter and fainter

“nebulae”)

The metric is given by

ds2 = −dt2 +R2(dχ2 + sin2 χdθ2 + sin2 χ sin2 θdφ2)︸︷︷︸3-sphere

– static cylinder

Closed Universe – finite total volume V = 2π2R3


Cosmological model of Einstein

Plug this metric into theEinstein’s equation:

Rµν −1

2gµνR−Λgµν = 8πGTµν

Tµν = diag(ρ,−p,−p,−p)

The solution exists ifcosmological constant andmatter are related as

Λ =1

R2, ρ =

2

8πGR2

Total mass of the Universe M = ρ · 3π2R3 = πR2G

Everything is a function of density that can be measuredexperimentally⇒full solution of the Universe constructed?


Cosmological model continued

de Sitter (1917) finds a different solution

ds2 = −R2 cos2 χdt2 +R2(dχ2 + sin2 χdθ2 + sin2 χ sin2 θdφ2)︸︷︷︸3-sphere

To satisfy GR equations this requires

Λ =3

R2, ρ = 0

– curved Universe without matter??


Cosmological model continued1922

Friedmann write the general ansatz for homogeneous andisotropic metric

ds2 = −dt2+a2(t)

(dχ2

1− κχ2+ χ2dθ2 + χ2 sin2 θdφ2

), κ = −1, 0, 1

Three homogeneous and isotropic spaces (κ – sign of curvature)



Plug this metric into the Einstein’s equation, using the general formof the stress-energy tensor being

Tµν = diag(ρ,−p,−p,−p)

The Eistein’s equations relate “matter” (some functions ρ(t) andp(t)) with the dynamics of the scale factor – Friedmann equation:

a2(t)

a2(t)≡ H2(t) =

8πG

3ρ− κ

a2

1922-1924

Second Friedmann equation:

a

a= −4πG

3(ρ+ 3p)



Energy conservation:

∂ρ

∂t= −3H(ρ+ p) = −3

a

a(ρ+ p)

Lemaıtre rediscovers these equations

Main predictions: the Universe is expanding. Static Universe wouldrequire very specific equations of state (ρ = −κ 3

8πGR2static and ρ =

−3p). Such a solution will be nevertheless unstable

Problems 1a-1c


Cosmology in a couple of words

Matter-dominated Universe: p = 0 and ∂ρ∂t = −3Hρ or ρa3 = const

and a ∝ t2/3

Radiation-dominated Universe: p = 13ρ and ∂ρ

∂t = −4Hρ or ρa4 =

const and a ∝ t1/2

Temperature T ∝ a−1. In radiation-dominated epoch ρ = π2

30gEFFT4

Einstein’s Λ-term: ρ(t) = −p(t) = const, a = e√

Λ3 t

Hubble equation — interplay between kinetic energy Ek = a2

2 andpotential energy Ep = −GMa(t) :

a2

2− G

4π3 ρ(t)a3(t)

a(t)= −κ

2


Hubble expansion

Slipher discovers redshifts of the spectral lines in the nearbygalaxies . De Sitter speculates for the first time that this can be 1912-1913

due to cosmological expansion in his model

Hubble discovers that “spiral nebulae” are far from us (M31, M33) 1925

Hubble estimates the distance to the nearby galaxies andestablishes redshift-distance relation 1926

cz = H0r


Hubble constant history

https://www.cfa.harvard.edu/˜dfabricant/huchra/hubble


https://www.cfa.harvard.edu/~dfabricant/huchra/hubble

Expansion of the Universe – the first pillar ofcosmology


Reminder: redshift

Universe stretches:

1 + z ≡ λobserved

λemitted=a(tobs)

a(temit)

Doppler effect:a galaxy is receding

1 + z ≡ λobserved

λemitted=

√1 + v/c

1− v/c

where Hubble velocityv = H0 × distance


The initial state of the Universe

The initial state of the Universe remained a problem

If Universe is filled with cosmological constant – its energydensity does not change

If Universe is filled with anything with non-negative pressure: thedensity decreases as the Universe expands

In the past the Universe was becoming denser and denser, ρ ∝ 1t2

,=⇒ ultradense cold state of the initial Universe?

High density baryonic matter — a Universe-size neutron star?Neutrons cannot decay anymore (n → p + e + νe) as thereare no available Fermi levels for fermions. The state is stableand remains such until cosmological singularity (ρ ∝ 1/tn)

Problems 1c,2a,5a


The Universe in the past

The origin of elements (Hydrogen, Helium, metals) remained achallenging problem 1920s-1930s

See e.g.review byZel’dovich,Section 13

Ultradense (ρn ∼ 1g/cm3) neutron star would mean that no hydrogenis left (as soon as density has dropped to allow neutron decay n→ p+e+ νe,each proton is bombarded by many neutrons so that p+ n→ d+ γ, d+ n→t+ γ) Zel’dovich in

Wikipediaorhere


http://lorentz.leidenuniv.nl/~iakubovskyi/Zeldovitch63.pdf




http://en.wikipedia.org/wiki/Yakov_Borisovich_Zel'dovich

http://en.wikipedia.org/wiki/Yakov_Borisovich_Zel'dovich

http://xray.sai.msu.ru/~mystery/html/Z/z.engl.html

Binding energy


Nucleosynthesis

If (as people thought) the density of plasma, needed for nuclearreactions to take place was ρ ∼ 107 g/cm3⇒very rapid expansionof the Universe (age ∼ 10−2 sec). Not enough to establish thermalequilibrium? Paper by

Gamow (1946)

Paper byGamow (1948)

Gamow suggested: consider the plasma temperature Td ∼ 109 K(∼ 100 keV)

He computed the total energy density of radiation as

ρrad = σSBT4 = 8.4 g/cm3

(T

109 K

)4

Gamow then assumed that the energy density of the Universe isdominated by radiation and estimated its age as

ρrad =3

32πGN

1

t2or t [sec] ∼ 1

(T [MeV])2


http://prola.aps.org/abstract/PR/v70/i7-8/p572_2

http://prola.aps.org/abstract/PR/v70/i7-8/p572_2

http://prola.aps.org/pdf/PR/v74/i4/p505_2


Nucleosynthesis

Gamow estimates the density of matter by comparing reaction rateand expansion rate of the Universe:

(v nσp+n→d+γ)−1

︸︷︷︸time between p-ncollisions

∼ td

Using σ ∼ 10−29 cm2, thermal velocity v ∼√

Tm, one gets n(i)

b ∼1018 cm−3 and therefore ρ

(i)b ∼ 10−6 g/cm3 ⇒the Universe was

radiation dominated!

Cross-section is the effective area that each incoming particle ”sees” – theprobability of some scattering event.

The number of photons at temperature Td is given by

nγ =2ζ(3)

π2T 3d ≈ 1028 cm−3

(T

109 K

)3

(1)


Nucleosynthesis

Prediction of the Gamow’s theory: baryon-to-photon ratio ηB ≡nbnγ∼ 10−10


Relic radiation

If so, what is the temperature of radiation bath today? For Gamow(also Alpher, Herman – a series of papers, see detailed account inPeebles) the density at z = 0 was n(0)

b ∼ 10−5 cm−3

Hubble constant estimates were higher than today and all matter today wasconsidered to be baryonic. So H2

0 = 8πG3 ρb

na3 ≈ const and Ta ≈ const (indeed, for radiation ρ ∝ T 4 and ρ ∝ a−4)

Therefore T (0) ∼ 109 K

(n

(0)b

n(i)b

)1/3

∼ 20 K

In reality the number density of baryons today is n(0)b ∼ 10−7 cm−3 which would

give Tcmb ∼ 5 K based on the above estimates

⇒the Univese today should be filled with radiation whosespectrum peaks at λ = 2.9 mm·K

T


Formation of structures

The Universe was hot (radiation-dominated at epoch ofnucleosynthesis. But the density of radiation dropped faster thanthe density of matter:

ρradρb∼ 1

a

⇒matter-radiation equality (at T ∼ 103 K!)

The growth of Jeans instabilities did not start until that matter-dominated epoch (see below)

Gamow estimates the size of the instability as Paper byGamow (1948)

kBTeq ∼GNρmatterR

3

R

Putting in the Teq ∼ 103 K one gets R ∼ 1 kpc similar to a typicalgalaxy size(!)




Hot Big Bang theory was born


Challenges to Hot Big Bang

In 1950s this was not so obvious!

There was no relict radiation from recombination

You should get about 30% of Helium (which was considered to be wrong,as its abundance was measured ∼ 10%)

In low density hot matter you cannot produce heavy nuclei (A = 5and A = 8) in this way. With Hubble constant at that time H0 ∼500km/sec/Mpc the age of the Universe ≈ the age of the Earth⇒heavy elements could not be produced in stars, should be in theUniverse “from the very beginning”.

Problems 5c for H0 = 500 km/sec/Mpc

It was concluded by many that “Hot Big Bang” is ruled out see e.g.Zel’dovichUFN 1963





Cosmic Microwave background

Accidentally discovered by Arno Penzias and Robert Wilson: 1965


COBE

Data from COBE (1989 – 1996) showed a perfect fit between the blackbody curve and that observed in the microwave background.


CMB spectrum

Cosmic microwave background radiation is almost perfect blackbody

CMB temperature T = 2.725 K


Properties of CMB

Temperature of CMB T = 2.725 K

CMB contribution to the total energy density of the Universe:Ωγ ' 4.5× 10−5

Spectrum peaks in the microwave range at a frequency of160.2 GHz, corresponding to a wavelength of 1.9 mm.

410 photons per cubic centimeter

Almost perfect blackbody spectrum (δT/T < 10−4)

COBE has detected anisotropies at the level δT/T ∼ 10−5

Go to CMB anisotropies section


Predictions of Hot Big Bang model

CMB

Baryon-to-photon ratio from BBN and CMB (independently)

Primordial abundance of light elements. Most notably, 4He

These predictions are consistent and allow fornon-trivial experimental cross-checks

Let us look at the BBN in more details


Nuclear network

To produce chemical elements one needs to pass through“deuterium bottleneck” p+ n↔ D + γ


Deuterium bottleneck

We saw that for each baryon there were ∼ 1010 photons.

Binding energy of deuterium isED = 2.2 MeV (or TD = 2.5×1010 K).

At T = ED 85% of all photons haveE > TD⇒any deuterim nucleuswill be quickly photo-disassociated via D + γ → p+ n

Production of deuterium becomes efficient when temperature dropsso that the number of photons with E > ED will be ∼ 10−10

nγ(E > ED)

nγtot∼ ηB =⇒ ηB

(2.5TBBNmp

)32

eED

TBBN ∼ 1 (2)

TBBN ≈ 70 keV and tBBN =M∗Pl

2T 2BBN

≈ 120s


Neutron/proton ratio

How many neutrons and protons are there (so far we did not distinguishbetween them)

At high temperatures chemical equilibrium between protons andneutrons is maintained by weak interactions n + ν p + e−,n+ e+ p+ ν, n p+ e− + νe

Description of these processes is given by Fermi 4-fermion theory:

LFermi = −GF√2

[p(x)γµ(1− γ5)n(x)][e(x)γµ(1− γ5)ν(x)] (3)

Fermi coupling constant GF ≈ 10−5 GeV−2

Problem: demonstrate the dimensionality of the Fermi coupling constant


The content of MeV plasma

If temperatures was at least few MeV, we expect plasma to containelectron-positron pairs in equilibrium amounts (γ+ γ e+ + e− forT & me)

We also know that the plasma contained some number of protonsand neutrons (their origin will be discussed later)

Weak reactions were in equilibrium until T ∼ 1 MeV

Many weak reactions that produce neutrinos (νe) are responsible forkeeping p and n in thermal equilibrium

p+ e− n+ νe n+ e+ p+ νen p+ e− + νe


Cross-section, reaction rates

Cross-section (in units length2) in 2→ 2 reactions is defined as

σ ∼∫

d3k

(2Ep)(2π)3

d3k′

(2Ek′)(2π)3|M|2δ4(

∑

in

p−∑

out

k)

where |M|2 is a matrix element – probability of scattering – for a particularchoice of incoming and outgoing momenta pin and kout

cross-section can depend only on Lorentz invariant quantities– masses of particles– coupling constants– 3 Lorentz-invariant combinations of incoming and outgoing

momenta, Mandelstam variables:

s = (p+ p′)2 = (k + k′)2 = 4E2cm

t = (k − p)2 = (k′ − p′)2

u = (k − p′)2 = (k′ − p)2



If all incoming particles are relativistic, E m, we expect that totalcross-section is a function of center-of-mass energy only

Example: QED

σ ∼ α2

E2cm

the real answer e.g. for e+ + e− → γ + γ is given by σ = πα2

2E2cm

up to somelog(E/me) corrections

Example: Fermi theory. Coupling constant GF has dimension[GF ] = GeV−2, cross-section [σ] = GeV−2.

σ ∼ G2FE

2cm

To check whether these reactions are in equilibrium, comparedscattering rate due to Fermi interaction with the Hubble expansionrate:

Γ ∼ G2FT

3



For reactions with neutrons and protons one should also take intoaccount that they are not relativistic and their number density isgiven by Boltzmann distribution.

These reactions go out of equilibrium at Tν ≈ 1 MeV

The difference of concentrations of n and p at that time is

nnnp

= exp

(−mn −mp

Tν

)≈ 1

6

mn −mp = 1.2 MeV

Almost all neutrons will end up in 4He. The mass abundance ofHelium is

Yp ≡4nHenn + np

=4(nn/2)

nn + np=

2(nn/np)

1 + nn/np

If ηB ∼ 1, Helium abundance would be 1/31+1/6 ≈ 0.28



However, as we saw due to ηB 1 formation of deuterium(preceeding formation of Helium) does not happen until T ∼ 70 keV

Therefore there is a time-delay between freeze-out of weak reactionand time of Helium formation. The unstable neutrons (lifetimeτn ∼ 900 sec decay and therefore by the time of Helium formationnn/np ≈ 1/7, which gives Yp ≈ 25%

⇒4He is the second most abundant element in the Universe (afterhydrogen)

The Helium abundance is known with a precision of a few% (e.g.Yp = 0.2565±0.0010(stat.)±0.0050(syst,)) and is indeed very close Izotov &

Thuan (2010)to 25%


CMB

As temperature of the Universe drops, all protons will recombinewith electrons to form neutral hydrogen: e + p → H + γ. Bindingenergy EH = 13.6 eV

If ηB 1 at T ∼ 13.6 eV for each hydrogen atom there are manyionizing photons.

As in the case of BBN and deuterium production, the temperatureshould drop significantly so that the number of energetic photons issmall

To find the number of “fast” photon, we describe high-energy tailof Bose-Einstein distribution as f(k) ≈ 1/(2π)3 exp[−k/T ] and findthe temperature when

nγ(E > EH)

nγ,tot≈ ηB (4)


CMB

This gives the solution Tdec ∼ EH/23 ≈ 0.6 eV

Again, knowing Tdec and Tcmb today (Tcmb = 2.725 K), one canindependently determine the baryon-to-photon ratio and confirmthe BBN prediction


BBN predictions confirmed

Curves – theoreticalpredictions of Big Bangnucleosynthesis

Horizontal stripes –values that follow fromobservations.

Golden stripe – measuredvalue of η from CMBobservations!


BBN and particle physics

Nowadays BBN has become a tool to determine properties(bounds) on light particles/decaying particles/evolution of fundamentalconstants

The Helium abundance is known with a precision of a few% (e.g.Yp = 0.2565± 0.0010(stat.)± 0.0050(syst,)) Izotov &

Thuan (2010)

Neutron lifetime provides a “cosmic chronometer”, measuring thetime between Tν (temperature of freeze-out of weak reactions) and Td(temperature of deuteron production):

nnnp

∣∣∣∣Td

=nnnp

∣∣∣∣Tν

e−t/τn

This time depends on the temperature Td and number of relativisticspecies at that time


Effective number of relativistic d.o.f.

Total energy density at radiation dominated epoch (i.e. the Hubbleexpansion rate/lifetime of the Universe) depends on the effectivenumber of relativistic degrees of freedom:

3

8πGNH2 = ρrad =

π2

30g∗T

4 or

where the number of relativistic degrees of freedom is given by

g∗ =∑

boson species

gi +7

8

∑

fermion species

gi

where relativistic species (having 〈p〉 & m) count

Problems 6b, 6d


BBN and particle physics

The primordial Helium abundance may change if

There are more than 3 neutrino species (Roughly: one extra neutrino ora particle with similar energy density is allowed at about 2σ level)

There was any other particle with the mass MeV and lifetime ofthe order of seconds or more that was contributing to g∗ at BBNepoch (1 second – lifetime of the Universe at T ∼ 1 MeV)

There were heavy particles with lifetime in the range 0.01 – fewseconds (that were decaying around BBN epoch)

Newton’s constant (entering Friedmann equation) changed betweenBBN epoch and later times (e.g. CMB or today)


NEUTRINO IN THE EARLY

UNIVERSE


Neutrino properties

there are 3 neutrinos (for each generation): νe, νµ, ντ

neutrinos are stable

neutrinos are electrically neutral

neutrinos have tiny masses (much smaller than mass of theelectron)

neutrinos participate in weak interactions

How neutrinos are produced in the early Universe?


Neutrinos in primordial plasma

Neutrino reaction rates?

Recall: weak interaction strength is Fermi coupling constantGF ≈ 10−5 GeV−2

In the processes like e+ + e− → να + να the interaction rate

Γee→νν = ne(T )× σWeak

whereσWeak ∝ G2

F × E2e

What is the typical energy of electrons in this reaction?


If in the expanding Universe particles that are in thermal equilibriumhave either Fermi-Dirac or Bose-Einstein distributions

At temperatures T m electron distribution function is

fe(p) = 4

∫d3p

(2π)3

1

ep/T + 1

Number density of the electrons

ne(T ) = 4

∫d3p

(2π)3

1

ep/T + 1∝ T 3

Average energy of the electron Ee = c× 〈p〉 i.e

Ee =4

ne(T )

∫d3p

(2π)3

p

ep/T + 1∼ T


As a result Ee ∼ T

Reaction rate Γee→νν ∼ G2FT

5

Compare the characteristic interaction time Γ−1ee→νν with the age of

the Universe tUniv = 1/H(T ). To establish equilibrium we needΓ−1ee→νν tUniv or Γee→νν H(T )

At what temperatures neutrinos are in equilibrium?

One can see that temperature when

Γ ∼ G2FT

5 = T 2

√8πGN

3g∗(T )

is roughly Tdec ∼ 1 MeV


g∗ in Standard Model

The Friedmanns equation for RD epoch can be written as:

H2(T ) =8πGN

3g∗(T )

π2

30T 4

︸︷︷︸ρrad

where g∗ – effective number of relativistic degrees of freedom.

As a result, 2 . g∗ . 110 for Standard Model:


Neutrino in the early Universe: summary

We saw that

Neutrinos are produced in the early Universe and are in thermalequilibrium in plasma at T & Tdec ∼ 1 MeV

As all equilibrium ultra-relativistic particles their average energy is〈Eν〉 ∼ T , their number density is ∼ T 3

Their interaction rate with other particles Γν ∼ G2FT

5

What happens below Tdec?


Freeze-out

If Γ . H particle go out of thermal equilibrium – freeze-out.

After the freeze-out, the comoving number density is conserved(particles are no longer produced or destroyed):

nco(T > Tdec) = nco(Tdec) ∝ T 3dec

The average momentum of decoupled particles changes with time(redshifts). Average momentum at the time of decoupling was ∼1 MeV. Average momentum today is ∼ 10−3 eV

As a result today in the Universe there are lots (about 100 cm−3)neutrinos (exercise: reproduce this number)

Their energy density today:

ρν =∑

mν × n or numerically Ωνh2 ≈

∑mν

94 eV


THE NATURE OF DARK MATTER


Dark Matter in the Universe

Stellar Disk

Dark Halo

Observed

Gas

M33 rotation curve

Expected: v(R) ∝ 1√R

Observed: v(R) ≈ const

Expected:masscluster =

∑massgalaxies

Observed: 102 times more massconfining ionized gas

Lensing signal (direct massmeasurement) confirmsother observations

Jeans instabilityturned tiny densityfluctuations into allvisible structures


Do we believe that DM exists?

Stellar Disk

Dark Halo

Observed

Gas

M33 rotation curve

Back to DM Newton dynamics: V(R) ∼ 1√R


Intracluster gas

Cluster Abell 2029. Credit: X-ray: NASA/CXC/UCI/A.Lewis et al. Optical: Pal.Obs. DSS

Dark Matter ∼ 85%Intracluster gas ∼ 15%Galaxies ∼ 1%

DM in clusterBaryons in cluster

≈ ΩDM

Ωbaryons

Temperature of ICM: 1− 10 keV ∼ 107 − 108 K

Back to DM page


Gravitational lensing


Dark Matter in the Universe

These phenomena are independent tracers of gravitationalpotentials in astrophysical systems. They all show that dynamicsis dominated by a matter that is not observed in any part ofelectromagnetic spectrum.

Stellar Disk

Dark Halo

Observed

Gas

M33 rotation curve


"Bullet" cluster

Cluster 1E 0657-56Red shift z = 0.296

Distance DL = 1.5 Gpc


Merging system in the plane of the sky? Subclusterpassedthrough thecenter ofthe maincluster.

? DM andgalaxies arecollisionless.

? Gashas beenstrippedaway (shockwave, MachnumberM = 3.2

andTshock ∼30 keV)


Mass determined via gravitational lensing

? Comparingthe weakgravitationallensing datawith velocitydistribution forgalaxies


Cosmological evidence for dark matter

We see the structures today and 13.7billions years ago, when the Universe was380 000 years old (encoded in anisotropiesof the temperature of cosmic microwavebackground)

All the structure is produced from tinydensity fluctuations due to gravitationalJeans instability

In the hot early Universe beforerecombination photons smeared outall the fluctuations

The structure has formed already, δρ/ρ ∼ 1 has to be long ago.i At CMB δρ/ρ ∼ 10−5, then grow δρ/ρ ∼ a (matter domination)

atodayadec

= 1 + zdec ∼ 103 Not enough!Go to CMB + Structure formation part


A few basic questions

Is evidence for DM convincing?Yes

There are still other options nevertheless

Is DM made up of particles?Plausible assumption .

But no hard evidence. More exotic possibilities such as primordial black holes orMACHOs are not completely ruled out

We will study the scenario of dark matter particle and itsconsequences for particle physics.


Properties of a DM candidate

DM is not baryonic

DM is not a SM particle (neutrinos could be but . . . )

Any DM candidate must be

– Produced in the early Universe and have correct relic abundance

– Very weakly interacting with electromagnetic radiation (“dark”)

– Be stable or cosmologically long-lived

There are plenty of non-SM candidates


Neutrino Dark Matter?

In 1979 when S. Tremaine and J. Gunn published in Phys. Rev. Lett.a paper “Dynamical Role of Light Neutral Leptons in Cosmology”

– The smaller is the mass of Dark matter particle, the larger is thenumber of particles in an object with the mass Mgal

– Average phase-space density of any fermionic DM should besmaller than density of degenerate Fermi gas

⇒ If dark matter is made of fermions – its mass is bounded frombelow:

Mgal4π

3R3

gal

14π

3v3∞

≤ 2mDM4

(2π~)3

[0808.3902]

Objects with highest phase-space density – dwarf spheroidalgalaxies – lead to the lower bound on the fermionic DM mass

MDM & 300− 400 eV


Neutrino Dark Matter?

However, if you compute contribution to DM density from massiveactive neutrinos (mν . MeV), you get

Ων DMh2 =

∑mν

∫d3k

(2π)3

1

ekT + 1

=

∑mν[eV]

94 eV

Using minimal mass of 300 eV you get ΩDMh2 ∼ 3 (wrong by about

a factor of 30!)

Sum of masses to have the correct abundance∑mν ≈ 11 eV

Massive Standard Model neutrinos cannot be simultaneously“astrophysical” and “cosmological” dark matter: to account for themissing mass in galaxies and to contribute to the cosmological

expansion


Neutrino dark matter

If at some moment neutrino decoupled there exists a cosmologicalneutrino background whose comoving number density is

nCNB ∝ T 3dec ν

Neutrinos are massive and become non-relativistic in the matter-dominated epoch

As neutrinos are massive they contribute to the total matter densityΩM today

DM particles erase primordial spectrum ofdensity perturbations on scales up to the DMparticle horizon – free-streaming length

λcoFS =

∫ t

0

v(t′)dt′

a(t′)

Comoving free-streaming is approximately equal to the horizon atthe time of non-relativistic transition tnr (when〈p〉 ∼ m)



Neutrino DM would homogenize the Universe at scales belowλcoFS > 1 Gpc. This contradicts to the observed large scale structure

and data on CMB anisotropies



DM particles erase primordial spectrum ofdensity perturbations on scales up to the DMparticle horizon – free-streaming length

λcoFS =

∫ t

0

v(t′)dt′

a(t′)

Comoving free-streaming is approximately equal to the horizon atthe time of non-relativistic transition tnr (when〈p〉 ∼ m)

Upper bound on neutrinomasses

∑mν < 0.58 eV

(WMAP+LSS, 95% CL).

Neutrinos are relativistic after recombination (znr < 850)

Neutrino DM would homogenize the Universe at scales belowλcoFS > 1 Gpc. This contradicts to the observed large scale structure

and data on CMB anisotropies


Properties of a DM candidate

DM is not baryonic

DM is not a SM particle (neutrinos could be but . . . )

Any DM candidate must be

– Produced in the early Universe and have correct relic abundance

– Very weakly interacting with electromagnetic radiation (“dark”)

– Be stable or cosmologically long-lived

There are plenty of non-SM candidates


Interactions of a DM candidate

DM interacts with the rest of the matter gravitationally

Other possible interactions?

It is possible that DM particles interact only in the early (very) hotUniverse with some unknown particles

To be produced from the SM matter the DM particles should interact

It may be absolutely stable and interact with SM particles viaannihilation only: DM+DM→SM. . .

It may decay with very small rate, ensuring cosmologically long life-time: DM→SM. . .

Go back


Example : WIMPs

Example: Non-relativistic weaklyinteracting particles


Weakly interacting massive particles

Consider weakly interacting neutral particles (as neutrinos) but withthe mass mχ MeV. These particles would be non-relativisticwhen they decouple

In this case, their number density at temperatures Tdec T mχ

is given by the Boltzmann distribution:

neqX (T ) =

(mχT

2π

)3/2

e−mχ/T , T ≥ Tdec

At later times (T < Tdec) the comoving number density of particlesis conserved:

nχ(T ) = nχ(Tdec)

(T

Tdec

)3

neqχ (T )

– freeze-out (At T < Tdec the number density of these particles is muchlarger than equilibrium (for a temperature T ))


WIMP freeze-out

We need to find the temperature of decoupling (of freeze-out) Tdec,such that

H(Tdec) = Γ(Tdec) ≡ 〈σv〉n(Tdec)

(for neutrino we took v = c = 1). Assuming mχ Tdec we can estimate〈σv〉 ∼ σ0 ×

√T/mχ where σ0 ∼ G2

Fm2χ (Ecm ∼ mχ).

Therefore we arrive

T 2

M∗= σ0

√T

mχ

(mχT

2π

)3/2

e−mχ/T

mχ

Tdec' log

(M∗mχσ0

(2π)3/2

)∼ log

(M∗m

3χG

2F

(2π)3/2

)

We see that e.g. for GeV scale particles and weak cross-sectionsmχ Tdec. Therefore, these particles indeed decouple non-relativistically, as we assumed.


WIMP freeze-out

The number density of X-particles at the moment of their decouplinggets diluted due to the expansion of the Universe which gives theirpresent-day number desnity

nχ,0 =

(afa0

)3

nχ(Tdec).

Using the conservation of comoving entropy we rewrite it as

nX,0 =

(s0

sf

)nχ(Tdec),

where s0 = 2× 4π2

90

(T 3γ + 3× 7

8 × T 3ν

)≈ 2.8× 103 cm−3 is the present-

day entropy of the Universe, sf = g∗(Tdec) × 4π2

90 T3dec is the entropy at

the time of decoupling.


WIMP freeze-out

Finally, the present-day abundance of X-particles is

ρχ = mχnχ,0 ∼ mχT 2dec

M∗σ0

s0

T 3dec

∝ log(σ0mχ)

σ0

and abundance

Ωχ =ρχρcrit

= 3× 10−10

(1 GeV2

σ0

)1√

g∗(Tdec)log

(MPl∗mχσ0

(2π)3/2

).

Note that this expression depends on mχ only logarithmically. Notealso the strong dependence on σ0: the weaker is the interaction, themore particles is created.


WIMP "miracle"

Taking electroweak cross-section

σ0 'α2W

M2W

' 10−7 GeV−2

mass Mχ = 100 GeV, g∗(Tdec) = 100, the log value is ' 30, so that forelectroweak-scale interaction one would obtain Ωχ ' 10−2. Thus wepredict DM abundance within an order of magnitude.

Thus, weakly-interacting massive particles (WIMPs) are consideredas probable dark matter candidates.

WIMPs can be searched in direct detection experiments (interactionof galactic WIMPs with laboratory nucleons). back


Another example.

Sterile neutrinos: a minimal unified modelof all observed BSM phenomena.


νMSM: all masses below electroweak scale

Just add 3 right-handed (sterile) neutrinos NIR to MSM: Asaka,

Shaposhnikov,PLB 620, 17(2005)LνMSM = LSM + iN

IR ∂/NI

R −(LαM

DαIN

IR +

MI

2(N

IR)cNIR + h.c.

)

10−6

10−2

102

106

1010

10−6

10−2

102

106

1010tcu

bs

d

τ

µ

ννν

N

NN

N

N

e 1

1

3

3

1

2

3

Majorana masses

massesDirac

ν

quarks leptons

2NeV

The spectrum of the MSM

ν

ν

ν

2


νMSM: all masses below electroweak scale

A very modest and simple modification of the SM which can explainwithin one consistent framework

X . . . neutrino oscillations

X . . . baryon asymmetry of the Universe

X . . . provide a viable (warm or cold) Dark Matter candidate

This model may be verified by existing experimentaltechnologies. It is importnat to confirm it or rule it out.


Searching for decayingdark matter


Decaying DM

DM with radiative signatures: DM → γ + ν, γ + γ, e+ + e− . . .

νNs

e± ν

W∓

γW∓

•

(a)

ℓ ℓ

ν

p− k

G

p

γ

k

ℓ

6R

•

(b)

ℓ ℓ

ν

p− k

G

p

γ

k

ℓ 6R


Decaying DM

Appears in many models:

Right-handed neutrinoDodelson & Widrow’93;Asaka, Shaposhnikov et al.’05

Gravitino with broken R-parityTakayama & Yamaguchi’00Buchmuller’07

Volume ModulusQuevedo’07


Monochromatic line in X-ray observations

DM decay should produce a linein X-ray spectra of various objects.

It should be visible against e.g powerlaw spectrum of diffuse extragalacticbackground.


Properties of decaying DM

The properties of decaying DM are much less studied.

Crucial property: the flux from DM decay

FDM =Eγ

mDM

ΓMfovDM

4πD2L

≈ ΓΩfov

8π

∫

line of sight

ρDM(r)dr (z 1, Ωfov 1)

The flux FDM ∼∫ρDM(r)dr and NOT to

∫ρ2

DM(r)dr, as in the case

of annihilating DM.

The difference is HUGE.


Decay signal from MW-sized galaxyMoore et al.2005


Annihilation signal from MW-sized galaxyMoore et al.2005


Decay vs. annihilation

In the case of decaying Dark Matterthe signal, if detected, is easyto distinguish from astrophysicalbackgrounds

We have a lot of freedom in choosingobservation targets and, therefore, canunambiguously check DM origin of asuspicious signal.


For decaying DM "indirect"search becomes very

promising!


VELOCITIES OF DARK MATTERPARTICLES


Primordial properties of super-WIMPs

Feeble interaction strength of super-WIMP DM particles means thatin general they have not an equilibrium primordial velocity spectrum

For super-WIMPs primordial velocity spectrum carries theinformation about their production

In case of such DM particles free-streaming does not describe thesuppression of power spectrum back

1x10-3

2x10-3

3x10-3

4x10-3

0 1 2 3 4 5 6

q2 f(q

)

q/T

L= 2L= 4L= 6L= 8L= 10L= 12L= 14L= 16L= 25

0.1

1

1 30 1 10

Tra

nsfe

r fu

nction T

(k)

k [h/Mpc]

L= 0L= 2L= 4L= 6L= 8L= 10L= 12L= 14L= 16L= 25


Subhalo mass function

We see much less satellites than naively expected

Where are these “missing satellites”? Moore et al.’99

Maccio &Fontanot’09

Is suppression of number of substructures due to the free-streaming?


How to probe primordial velocities?

Effects of primordial velocities – not just a cut-off in matter powerspectrum at free-streaming scale

Primordial velocities affect:– Power-spectrum of density fluctuations (suppress normalization

at large scale)

– Halo mass function (number of halos of small mass decreases)

– Dark matter density profiles in individual objects

Scales probed by CMB experiments (linear regime of perturbationgrowth)

k ' `× H0

2=

`

6000

h

Mpc

Is sensitive up to scales k . 0.1 h/Mpc

Smaller scales?


Lyman-α forest and cosmic web

Image: Michael Murphy, Swinburne University of Technology, Melbourne, Australia

Neutral hydrogen in intergalactic medium is a tracer of overall matterdensity. Scales 0.3h/Mpc . k . 3h/Mpc


The Lyman-α method includes

Astronomical data analysis of quasar spectra

Astrophysical modeling of hydrogen clouds

N-body simulations of DM clustering at non-linear stage

Solving numerically Boltzmann equations for SM in the earlyUniverse

Finding global fit to the whole set of cosmological data (CMB, LSS,Ly-α), using Monte-Carlo Markov chains

Main challenge: reliable estimate of systematic uncertainties


Lyman-α forest and warm DM

Previous works (Viel et al.’05-’06; Seljak et al.’06) put bounds on free-streaming λFS . 100 kpc (“WDM mass” > 10 keV)

Pure warm DM with such free-streaming would not modify visiblesubstructures

In Boyarsky, Lesgourgues, Ruchayskiy, Viel’08 we revised these boundsand demonstrated that

Boyarsky+JCAP’09;PRL’09– The primordial spectra are not

described by free-streaming

– There exist viable models withthe mass as low as 2 keV,consistent with the Lyman-α

1 keV/m s

F WD

M

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.2

0.4

0.6

0.8

1


Halo (sub)structure in CDM+WDM universework inprogress


Halo (sub)structure in CDM universe


Halo (sub)structure in CDM+WDM universe

PRELIMINARY: Aq-A-2 halo in CDM and CDM+WDM simulations (Gao, Theuns, Frenk, O.R., . . . )

Simulated CWDM model (right) is fully compatible with the Lyman-αforest data but provides a structure of Milky way-size halo differentfrom CDM (left)


Window of parameters of sterile neutrino DM

Sin

2 (2θ)

MDM [keV]

10-16

10-14

10-12

10-10

10-8

10-6

0.3 1 10 100

Ω > ΩDM

Ω < ΩDM


Window of parameters of sterile neutrino DMBoyarsky,Ruchayskiy etal. 2005-2008

Sin

2 (2θ)

MDM [keV]

10-16

10-14

10-12

10-10

10-8

10-6

0.3 1 10 100

Excluded from X-rays


Window of parameters of sterile neutrino DMBoyarsky,Ruchayskiy etal. 2005-2008

Sin

2 (2θ)

MDM [keV]

10-16

10-14

10-12

10-10

10-8

10-6

0.3 1 10 100

Excluded from X-rays

Exc

lud

ed f

rom

PS

D e

volu

tio

n a

rgu

men

ts


Window of parameters of sterile neutrino DMBoyarsky,Ruchayskiy,Lesgourgues,Viel[0812.3256]

Boyarsky,Ruchayskiy,Shaposhnikov[0901.0011]

sin

2(2

θ 1)

M1 [keV]

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

5 50 1 10

ΩN1 < ΩDM

Ph

as

e-s

pa

ce

de

ns

ity

co

ns

tra

ints

X-ray constraints

ΩN1 > ΩDM

L6=25L6=70

NRP

L6max

=700BBN limit: L

6BBN

= 2500


Window of parameters of sterile neutrino DMBoyarsky,Ruchayskiy,Lesgourgues,Viel[0812.3256]

Boyarsky,Ruchayskiy,Shaposhnikov[0901.0011]

sin

2(2

θ 1)

M1 [keV]

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

5 50 1 10

ΩN1 < ΩDM

Ph

ase-s

pace d

en

sit

yco

nstr

ain

ts

X-ray constraints

ΩN1 > ΩDM

L6=25L6=70

NRP

L6max

=700BBN limit: L

6BBN

= 2500

Sterile neutrino is still viable and very attractive DM candidate. TheνMSM should be verified.

To explore the allowed window, more theoretical efforts, both onparticle physics and astrophysics sides, and new methods ofanalysis of the full set of the cosmological and astrophysical data isneeded.


Baryon asymmetry of the Universe

In general, all elementary particles can be divided into three groups:

Truly neutral, like photon, intermediate Z-boson, Majorana neutrino,π0, etc. They do not carry any charges.

Particles, like proton, neutron, and electron

Antiparticles, like antiproton, antineutron, and positron

CPT theorem: particles and antiparticles have the same mass, thesame lifetime, but opposite charges (electric, baryonic, leptonic, etc).

Naturally, a matter is a substance which consists of particles, andantimatter is a substance consisting of antiparticles.


Baryon asymmetry in the present universe

Main questions: Why do the Earth, the Solar system and ourgalaxy consists of of matter and not of antimatter?

Why we do not see any traces of antimatter in the universe exceptof those where antiparticles are created in collisions of ordinaryparticles?

This looks really strange, as the properties of matter and antimatterare very similar.


Antiprotons in the universe


Positrons in the universe


Baryon asymmetry of the Universe

There are two possibilities:

Observed universe is asymmetric and does not contain anyantimatter

The universe consists of domains of matter and antimatterseparated by voids to prevent annihilation. The size of thesezones should be greater than 1000 Mps, in order not to contradictobservations of the diffuse γ spectrum.

The second option, however, contradicts to the large scale isotropy ofthe cosmic microwave background.

Thus, we are facing the question: Why the universe is globallyasymmetric?


Matter-antimatter asymmetry in particle physics

Parity is broken in weak interactions

CP is conserved (ν(~v) −→ ν(−~v)

CP-violation in kaon decays (1964 Cronin, Fitch,. . . ) In a small fractionof cases (∼ 10−3), long-lived KL (a mixture of K0 and K0 decays into pair oftwo pions, what is forbidden by CP-conservation.

If CP were exact symmetry, an equal number of K0 and K0 wouldproduce an equal number of electrons and positrons in the reaction

K0 → π−e+νe, K0 → π+e−νe,

However, the number of positrons is somewhat larger (∼ 10−3) thanthe number of electrons.


Matter-antimatter puzzle

There is indeed a tiny difference between particles and antiparticles,on the level of 10−3, observed in particle physics experiments

How can this very small distinction betransformed in the 100% asymmetryof the universe we observe today?


Thermal history of baryon asymmetry

At t ∼ 10−6s after the big Bang for 1010 quarks we have (1010 − 1)antiquarks. Somewhat later the symmetric background annihilatesinto photons and neutrinos while the asymmetric part survives andgives rise to galaxies, stars, planets.

1

t10−6

s

n − n

n + n

B

B B

B

annihilation ofsymmetric background

ηB


Sakharov conditions

Sakharov: To generate baryon asymmetry of the Universe 3conditions should be satisfied

I. Baryon number should not be conserved

II. C-symmetry and CP-symmetry must be broken

III. Deviation from thermal equilibrium in the Universe expansion


Baryon number non-conservation

Baryon charge is conserved in particle physics processes. As aconsequence proton is stable (proton lifetime > 6.6× 1033 years fordecays such as p→ π0 + e+ or p→ π0 +µ+. This bound is 5× 1023

times longer than the age of the Universe

The conservation of baryon number would mean that the totalbaryon charge of the Universe remains constant in the process ofevolution.

If initial conditions were matter-antimater symmetric1 – no baryonasymmetry could have been generated without baryon numberviolation

1See the discussion of initial conditions below


C- and CP-non-conservation

C- and CP-symmetries change baryon number of particles:C |p〉 = |p〉, C |e−〉 = |e+〉, etc.

If these symmetries were conserved in the early Universe thiswould mean that for any process, changing baryon number, thereis another process, restoring baryon number. Namely, if

X1 +X2 + · · · → Y1 + Y2 + . . .

change baryon number by +1, then there is a process:

X1 + X2 + · · · → Y1 + Y2 + . . .

in which baryon number changes by−1 and their probabilities arethe same.


Deviation from thermal equilibrium

In thermal equilibrium for any process there is a reverse one

Asymmetries do not grow, moreover, they tend to decay

In the SM all the conditions seems to be satisfied:

– CP is violated

– Baryon number may not be non-conserved: it can be createdfrom lepton number by non-perturbative processes active at hightemperature

– There may be phase transitions ( E-W, QCD).

However, experimental bounds on the SM parameters show thatthis does not happen!

Back to beyond SM problems


Phase transitions in the early Universe

PHASE TRANSITIONS IN THE

EARLY UNIVERSE


Phase transitions

In the presence of the temperature, the potential for the field φ canchange:

V (φ) = λ

[φ4

4+φ2

2

(T 2

4− v2

)]

Tc = 2v

From http://www.phys.uu.nl/˜prokopec


http://www.phys.uu.nl/~prokopec

Phase transitions

Two main types of phase transitions:

I order – Discontinuity of 〈φ〉T (left).

II order – No discontinuity of 〈φ〉T (right).


1st order phase transition


2nd order phase transition

Back to Sakharov


Search for decaying DM: main challenges

Control of astrophysical andinstrumental background

Reliable determination of darkmatter content of an object


DM in Andromeda galaxy (2007)0709.2301

0.1

1

10

10 30 60 90 1 10

DM

co

lum

n d

ensi

ty (

g/c

m2 )

Off-center angle, arcmin

K2GFBGKING

MOOREN04

NFWBURK

KERM31AM31BM31C


Mass-to-light ratio in Andromeda galaxy?

Corbelli et al. A&A 2009

Chemin et al. ApJ 2009

Mass-to-light ratio of bulge and disk components vary by afactor ∼ 4


DM in Andromeda galaxy (2010)

Red -W & D, M31bGreen -W & D, M31cBlue -W & D, M31d

Dashed -Chemin09, ISODotted -Corbelli09, R_B = 28 kpc

5 10 15 20r,kpc

100

1000

500

200

300

150

700

S_DM, M_Sunpc^2Dark matter column density


DM distribution in individual objects

Knowledge of dark matter distribution in individual objects is crucialfor astrophysical searches of decay/annihilation signals

Dark matter column density is uncertain within a factor of few (muchmore for

∫ρ2dl)

Uncertainty in modeling of the baryonic contribution

Dwarf spheroidal galaxies PRL’06


Universal properties of DM distribution

Fortunately, it is possible to minimize the dependenceof the results on astrophysical uncertainties related toindividual objects.

One can exploit a universal property of DMdistributions.


Constant surface density?Kormendy,Freeman’94;Donato et al.2009;PRL’06

Dark matter surface density remains for different types of galaxies?


An evidence in favor of MOND?Gentile et al.Nature’09

Baryonic surface density for different types of galaxies.


Observations vs. simulations0911.1774S changesslowly.There is auniversalscaling.

0

1

2

3

4

5

6

7

107

108

109

1010

1011

1012

1013

1014

1015

1016

DM

co

lum

n d

ensi

ty,

lg (

S/M

sun p

c-2)

DM halo mass [Msun]

Clusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphsIsolated halos, ΛCDM N-body sim.Subhalos from Aquarius simulation

0

1

2

3

4

5

6

7

107

108

109

1010

1011

1012

1013

1014

1015

1016

DM

co

lum

n d

ensi

ty,

lg (

S/M

sun p

c-2)

DM halo mass [Msun]

M and S - caustics, clustersM and S - caustics, groupsM - caustics, S - X-raysM - WL, S - WLM - WL, S - X-rays

S ∼(Mhalo

)≈0.2



0

1

2

3

4

5

6

7

107

108

109

1010

1011

1012

1013

1014

1015

1016

DM

co

lum

n d

ensi

ty,

lg (

S/M

sun p

c-2)

DM halo mass [Msun]


0

1

2

3

4

5

6

7

107

108

109

1010

1011

1012

1013

1014

1015

1016

DM

co

lum

n d

ensi

ty,

lg (

S/M

sun p

c-2)

DM halo mass [Msun]

M and S - caustics, clustersM and S - caustics, groupsM - caustics, S - X-raysM - WL, S - WLM - WL, S - X-raysAverage data from WL

S ∼(Mhalo

)≈0.2

Go back to the intro


Universal properties of DM distributions?

Going through the literature we collected a “catalog” of ∼1000 DMBoyarsky et al.0911.1774

density profiles for ∼300 individual objects, ranging from dwarfspheroidal satellites of the Milky Way to galaxy clusters

Different methods (rotation curves, X-rays, weak lensing, . . . ). Differentobservational groups fit the mass distribution with different velocityprofiles (isothermal sphere, Navarro-Frenk-White, Burkert, . . . )

Important questions:

– What properties to compare?– Often fits to different DM density profiles exist for the same object.

How to relate their parameters?– Any universality is observed?


Comparing DM density profiles

Fitting the same (simulated) data with two different profiles onefinds a relation between parameters of two DM density distribution,fitting the same data 0911.1774

5 10 15 20

r

rc

0

4

6

8

10

12vc

2

HaL

– NFW vs. ISO :rs ' 6.1 rc; ρs ' 0.11 ρc

– NFW vs. BURK :rs ' 1.6rB ; ρs ' 0.37ρB

– For most observed objectsρ?r? = const

Observable not sensitive to the choice of dark matter density profile– Dark matter column density

§ =

∫

l.o.s.

ρDM(r)dl ∝ ρ?r?



0

1

2

3

4

5

6

107

108

109

1010

1011

1012

1013

1014

1015

1016

DM

colu

m d

ensi

ty, lg

(S

/Msu

n p

c-2)

DM halo mass [Msun]

Clusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphsIsolated halos from N-body simulationsSubhalos from Aquarius simulation

S ∼(Mhalo

)≈0.2


Universal scaling of DM column density

0.5

1

1.5

2

2.5

3

3.5

107

108

109

1010

1011

1012

1013

1014

1015

1016

DM

co

lum

den

sity

, lg

(S

/Msu

n p

c-2)

DM halo mass [Msun]

The relation between § and Mhalo is observed for isolated halos of 0911.1774

all scales (for all observed halo masses from 108M to 1015M).

Slope of subhalos (Aquarius simulation) is reproduced

The median value and scatter coincide remarkably well with puredark matter numerical simulations


Universal scaling of DM column density

0.5

1

1.5

2

2.5

3

3.5

107

108

109

1010

1011

1012

1013

1014

1015

1016

DM

co

lum

den

sity

, lg

(S

/Msu

n p

c-2)

DM halo mass [Msun]

No visible features – universal (scale-free) dark matter down to thelowest observed scales and masses

No deviations from CDM down to Mhalo = 1010M

new proof that dark matter exists!


Independent determination of mass

0

1

2

3

4

5

6

7

107

108

109

1010

1011

1012

1013

1014

1015

1016

DM

colu

mn d

ensi

ty, lg

(S

/Msu

n p

c-2)

DM halo mass [Msun]


0

1

2

3

4

5

6

7

107

108

109

1010

1011

1012

1013

1014

1015

1016

DM

colu

mn d

ensi

ty, lg

(S

/Msu

n p

c-2)

DM halo mass [Msun]

M and S - caustics, clustersM and S - caustics, groupsM - caustics, S - X-raysM - WL, S - WLM - WL, S - X-rays


Independent determination of mass

0

1

2

3

4

5

6

7

107

108

109

1010

1011

1012

1013

1014

1015

1016

DM

colu

mn d

ensi

ty, lg

(S

/Msu

n p

c-2)

DM halo mass [Msun]


0

1

2

3

4

5

6

7

107

108

109

1010

1011

1012

1013

1014

1015

1016

DM

colu

mn d

ensi

ty, lg

(S

/Msu

n p

c-2)

DM halo mass [Msun]

M and S - caustics, clustersM and S - caustics, groupsM - caustics, S - X-raysM - WL, S - WLM - WL, S - X-raysAverage data from WL


Qualitative understanding?

This behaviour can be understood qualitatively in the framework ofCDM

The sphere of influence of the DM halo (sphere of zero velocity,turn-around radius)

Rta ∝(GM

H2

)1/3

Self-similar density profiles: characteristic scale r? ∝ Rhalo whereRhalo ≈ Rta

ThereforeS ∝ ρ?r? ∝ ρtaRta ∝ c(M) ·M1/3

ta

Observationally, the “concentration parameter” c = r?/Rta is a weakfunction of mass


DM column density in infall model

0

1

2

3

4

5

6

107 108 109 1010 1011 1012 1013 1014 1015 1016

DM column density, log10[S/Msun pc-2]

DM halo mass M200 [Msun]

Subhalos from Aquarius simulationIsolated halos from ΛCDM N-body simulationsPredictions from the Secondary infall modelClusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphs

S ∼(Mhalo

)1/3−0.1

arxiv:0911.3396



This behaviour can be understood qualitatively in the framework ofCDM


Rta ∝(GM

H2

)1/3

Self-similar density profiles: characteristic scale r? ∝ Rhalo whereRhalo ≈ Rta

ThereforeS ∝ ρ?r? ∝ ρtaRta ∝ c(M) ·M1/3

ta



Restrictions on modifications of gravityA.Boyarsky,O.Ruchayskiy1001.0565

0

1

2

3

4

5

6

7

8

107 108 109 1010 1011 1012 1013 1014 1015 1016


DM halo mass [Msun]

Clusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphsNorm. branch, α = 0 ; rc = 150 MpcSelf-acc. branch, α = 0 ; rc = 150 MpcNorm. branch, α = 1/4 ; rc = 300 MpcSelf-acc. branch, α = 1/4 ; rc = 300 MpcBest-fit model S ∝ M0.23


Direct astrophysical detection.

As column density does not vary too much, decaying DM producesan all-sky signal with some hot spots.

Objects of different scales and nature can be used to put robustbounds.

Ones a candidate line is found, spacial distribution can becompared with DM column density map.

DM origin can thus be unambiguously checked.

For decaying DM"indirect" search becomes

"direct" !


Restrictions on sterile neutrino DMBoyarsky et al.MNRAS-2008

10-30

10-25

10-20

10-15

10-10

10-5

100 101 102 103 104

sin2 (

2θ)

Ms [keV]

XMMChandra

HEAO-1

SPI (INTEGRAL)

MWM31

MW

Galactic center


Restrictions on life-time of decaying DM

Boyarsky+ :XRB HEAO-12005;

Bullet clusterChandra 2006;

LMC XMMMW XMM2006-2007

MW ChandraRiemer-Sørensen+.;Abazajian+ 2007

M31Watson+ 2006;Boyarsky+ 2007

dSps(UMi,Draco,W1, Sc,Forn), Suzaku,Chandra, XMMBoyarsky+2006,2010;Loewenstein,Kusenko2008-2009

Life

-tim

e τ

[sec

]

MDM [keV]

1025

1026

1027

1028

1029

10-1 100 101 102 103 104

XMM, HEAO-1 SPI

τ = Universe life-time x 108

Chandra

PSD

exc

eeds

deg

ener

ate

Fer

mi g

as


New mission: EDGE/XENIA

Spectrometers with big FoV andspectral resolution better than10−3 are needed

Future missions (XEUS orConstellation X ) will have betterspectral resolution but verysmall FoV

XENIA (former EDGE),proposed for NASA’s CosmicOrigins by the team fromNASA/MSFC, INAF, SRON +ISDC, EPFL,. . . ).

ART−XSpectrometer @ 1 keVEDGE Low−Energy

@ 6 keVEDGE wide FoV

A.Boyarsky, etal. (2007)


THANK YOU FOR YOURATTENTION



Gravitational collapse: gravitational potential energy U ∝ GMR

balances kinetic energy of cosmological expansion K ∝ H2R2


Rta ∝(GM

H2(t)

)1/3

Self-similar solutions would give

S ∝ ρ?r? ∝ ρtaRta ∝ c(M) ·M1/3ta



DM column density in infall model

0

1

2

3

4

5

6

107 108 109 1010 1011 1012 1013 1014 1015 1016


DM halo mass M200 [Msun]

Subhalos from Aquarius simulationIsolated halos from ΛCDM N-body simulationsPredictions from the Secondary infall modelClusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphs

S ∼(Mhalo

)1/3−0.1

arxiv:0911.3396


Example: Lyman-α forest

Absorption lines of neutral hydrogen trace DM distribution atdifferent red-shifts

Neutral hydrogen absorption line at λ = 1215.67A

From the Earth observer point of view we see the forest:λ = (1 + z)1215.67A


Observational data


Parameters of Aquarius simulation

Name mp ε Nhr Nlr N50

[M] [pc]

Aq-A-1 1.712× 103 20.5 4,252,607,000 144,979,154 1,473,568,512Aq-A-2 1.370× 104 65.8 531,570,000 75,296,170 184,243,536

Basic parameters of the Aquarius simulations. mp is the particlemass, ε is the gravitational softening length, Nhr is the number of highresolution particles, and Nlr the number of low resolution particlesfilling the rest of the volume. M200 = 1.839 × 1012M is the virialmass of the halo, defined as the mass enclosed in a sphere withmean density 200 times the critical value. r200 = 245 kpc gives thecorresponding virial radius. M50 = 2.524× 1012M. Finally, N50 givesthe number of simulation particles within r50 = 433 kpc. Springel et

al.’08

Back to CDM+WDM halo simulation


Literature

A very interesting and instructive article about how the pro http://people.bu.edu/gorelik/cGh_Bronstein_UFN-200510_Engl.htm

Very nice lectures on cosmology and early universe

http://arxiv.org/abs/hep-ph/0004188


http://people.bu.edu/gorelik/cGh_Bronstein_UFN-200510_Engl.htm



http://arxiv.org/abs/hep-ph/0004188

Plan

1. May be some question about h and c, Bronstein. Question: whythe mass of electron is 511 keV, however the energy e2mc/~ = mc2.Renormalisability, QED, gravity. 2. Dirac equation, positron,

Quantum field theory: collection of free particles, interactions,perturbation theory.

3. Neutrino: the first particle found as missing energy.

4. The theory of beta decay (1934)(Cheng-Lie) . alpha decay ( stronginteractions).

First p, n, nu etc. Parity violation ( 1956-57) Then many other similarprocesses, more general Lagrangian ( V-A theory).

Weak and strong interactions? fast and slow. (definitions ?)


CMB anisotropies

PHYSICS OF COSMIC MICROWAVEBACKGROUND


CMB anisotropy map

CMB temperature is anisotropic over the sky with δT/TCMB ∼ 10−5

WMAP-5 results with subtracted galactic contribution (courtesy of WMAP Science team)


CMB anisotropies (cont.)

The temperature anisotropy δT (n) is expanded in sphericalharmonics Ylm(n):

δT (~n) =∑

l,m

almYlm(n)

alm’s are Gaussian random variables (before sky cut)

CMB anisotropy (TT) power-spectrum: 2-point correlation function

〈δT (n) δT (n′)〉 =∞∑l=0

2l + 1

4πClPl(n · n′)

Pl(n · n′) – Legendre polynomials

Multipoles Cl’s

Cl =1

2l + 1

l∑m=−l

|alm|2

probe correlations of angular scale θ ∼ π/l


WMAP + small scale experiments

The WMAP 5-year TT power spectrum along with recent results from the ACBAR(Reichardt et al. 2008, purple), Boomerang (Jones et al. 2006, green), and CBI(Readhead et al. 2004, red) experiments. The red curve is the best-fit ΛCDMmodel to the WMAP data.


What (how) can we learn from CMB?

back to DM


Intermission:structure formation basics


Evolution of structures?

How did the structures evolve fromthis ⇑ to this ⇓?


Structure formation

Total energy of the Universe

Etot =R2(t)

2−G(

4π3 ρR

3(t))

R(t)= 0

m

H2(t) =R2(t)

R2(t)=

8πG

3ρ

Friedmann equation

R(t)

ρ > ρ

Uniform density ρ

ρ < ρ

Will ollapse

into a galaxy

Will grow

into a void

Jeans instability in expanding Universe: interplay of twoconcurrent processes:

– Gravitational attraction within an overdense region(U ∼ GM

R

)

– Overall expansion of the Universe(K ∼ H2R2

2

)


Analytical model: spherical collapse

Constant density overdensity ρ inside expanding FRW Universewith the average matter density ρ(t) (assume for simplicity ΩDM =ΩM = Ωcrit)

Overdensity expands with the Universe until the pull of gravityovercomes the kinetic energy of cosmological expansion

ρ(tmax) =9π2

16ρ(tmax)

Overdensity recollapses and “virializes”, so that rvir = rmax/2 overa period of time tvir ≈ 2tmax

Finally, one obtains

ρ(tvir) =9π2

16× 8× 4ρ(tvir) ≈ 178ρ(tvir)


Analytical model: secondary infall

Evolution of the radius r(t) of a spherical shell is governed by theNewtonian dynamics

d2r

dt2=Gm(t)

r2,

– m(t) is the mass inside the radius r(t).

– Initial velocities follow Hubble flow r(ti) = H(ti)ri

For initial perturbations with power-law profiles δMiMi

=(M0Mi

)ε, the

halo density profie evolves in a “self-similar” manner

ρ(r, t) =M(t)

R3(t)× F

(r

R(t)

).

F (x) does not depend on mass/size


Secondary infall model: phase-spaceSikivie,Tkachev,Wang’96


Turn-around radius

Gravitational potential energy U ∝ GMR balances kinetic energy of

cosmological expansion K ∝ H2R2


Rta ∝(GM

H2(t)

)1/3

Grows with time while Hubble expansion decelerates

The density inside the turn-around radius is the same for objectsof all masses and is determined by cosmology

ρta(t) ∝ ρM(t)


Cosmic web

Gravitationally collapsing structures form a“cosmic web”

Relativistic particles free stream out ofoverdense regions and smooth primordialinhomogeneities

Overdensity


Jeans instability I

Consider Newtonian perfect fluid filling all the space

∂ρ

∂t+ ~∇ · (ρ~v) = 0

∂v

∂t+ (~v · ~∇)~v +

1

ρ~∇p+ ~∇φ = 0

~∇2φ = 4πGNρ

p – pressure, ρ – density, φ –gravitational potential

Homogeneous solution: ρ = ρ, ~v = 0, p = p0

Following Jeans we assume that uniform fluid, filling all space has φ = 0

Is it stable? Let ρ = ρ+ δρ, p = p0 + δp, etc. Find perturbed solution


Jeans instability II

Perturbations:

∂2δ

∂t2− v2

s∇2δ = (4πGN ρ)δ, δ ≡ δρ

ρ= e−iωt+i

~k·~x

ω2 = v2sk

2 − 4πGN ρ. , where vs – speed of sound.

Modes are unstable for k < kJ :

kJ =

(4πGN ρ

v2s

)1/2

Arbitrarily small perturbations of size bigger than λJ = 2πk−1J will

collapse under the pull of self-gravity


Jeans instability in expanding Universe

In non-expanding Universe Jeans unstable modes grow exponentiallyfast

Expansion slows down the growth of instabilities (i.e. pulls apartcollapsing structures)

How do structures collapse in expanding Universe?


Jeans instability in expanding Universe

Expanding Universe Non-expanding Universe

δ(τ) =δρ(τ)

ρ(τ)δ(t) =

δρ(t)

ρρ = const

ρ ∼ a−4 RDa−3 MD

ρ = const

δ+a

aδ+v2

s(k2−k2

J)δ = 0 derivatives

with respect to conformal time τδ + v2

s(k2 − k2

J)δ = 0

k2J =

4πGN ρ(τ)a2(τ)

v2s(τ)

k2J =

4πGN ρ

v2s

v2s(τ) = p(τ)

ρ(τ) =

≈ 1

3 RD≈ 0 MD

v2s = const

Perturbations grow at most power-like

Perturbations grow exponentially

δ(τ) ∼ a(τ) ∼ τ2δ(t) ∼ e

√4πGN ρt


Real CMB physics

Neutrinos

BaryonsDark

Matter

Metric

ComptonScattering

Coulom

b

Scattering

Photons Electrons

From S. Dodelson’s“Modern Cosmology”


Growth of perturbations

System of coupled Boltzmann equations

Radiation perturbations (δγ and tightly coupled to it δb at RD epoch)remain frozen in time (for scales larger than Jeans length)

Radiation perturbations oscillate (acoustic oscillations) for smallerthan Jeans length scales

In RD epoch DM perturbations grow only logarithmically in τ forsmall scales (kτ >

√3)

DM starts to grow after τeq – time when density of matter and

radiation equates: zeq =Ωγ+ΩνΩDM+Ωb

In MD epoch DM perturbations grow quadratically in τ


Cosmological parameters and CMB

0

1000

2000

3000

4000

5000

6000

7000

8000

500 10 100 1000

l(l+

1) C

l / 2

π [µ

K2 ]

l

ΩΛ = 0.7

Ωb = 0.05; Ωdm = 0.25

Ωb = 0.25; Ωdm = 0.0


Large scale structure


Free-streaming

Relativistic particles cannot be gravitationally bound

They free stream out of overdense regions and smooth primordialinhomogeneities on the scales below free-streaming horizon

λcoFS =

∫ t

0

v(t′)dt′

a(t′)=

∫ tnr

0

dt′

a(t′)+

∫ teq

tnr

dt′

a2(t′)+ . . .

Suppression mass scale: MFS =4π

3ρ

(λFS

2

)3

Go back to the neutrino DM page


Free-streaming (numbers)

Free-streaming length for fermions “almost” in equilibrium: Bond,Efstathiou,Silk

λFS = 1.2 Mpc( 〈p〉〈pν〉

)(1 keVmDM

)

The free-streaming mass:

MFS = 1.77M3Pl

m2DM' 2.9× 1012M

(1 keVmDM

)2

Go back to the neutrino DM page


Thermal relics

Thermal relics (sometimes called also generic warm dark matter )decouple relativistic and have Fermi-Dirac-like primordial velocitydistribution function

f(v) =1

1 + exp(mvTR)

Dark matter abundance ΩDMh2 =

mTR

94 eV

(TRTν

)3

The WDM transfer function is suppressed as

T (k) =(

1 +

(k

kFS

)2ν)−5/ν

, ν ≈ 1.2

The free-streaming scale kFS = 20.4h

Mpc

(mTR

keV

)1.11(

0.25× 0.72

ΩDMh2

)0.11

Go back to the primordial velocities page


TOCEarly Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1Thermal history of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Cosmological model of Einstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Cosmological model continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Cosmological model continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Cosmology in a couple of words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Hubble expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Hubble constant history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Reminder: redshift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14The initial state of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15The Universe in the past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Binding energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Relic radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21Formation of structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22Challenges to Hot Big Bang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Cosmic Microwave background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25COBE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26


TOC

CMB spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Properties of CMB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Predictions of Hot Big Bang model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Nuclear network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30Deuterium bottleneck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31Neutron/proton ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32The content of MeV plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Cross-section, reaction rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34CMB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38BBN predictions confirmed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40BBN and particle physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Effective number of relativistic d.o.f. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42BBN and particle physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Neutrino properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45Neutrinos in primordial plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47g∗ in Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Neutrino in the early Universe: summary . . . . . . . . . . . . . . . . . . . . . . . . . 50


TOC

Freeze-out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Dark Matter in the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Do we believe that DM exists? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54Intracluster gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55Gravitational lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56Dark Matter in the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Cosmological evidence for dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . 61A few basic questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Properties of a DM candidate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63Neutrino Dark Matter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Neutrino dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Neutrino dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Neutrino dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Properties of a DM candidate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69Interactions of a DM candidate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Example : WIMPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Weakly interacting massive particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72WIMP freeze-out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73


TOC

WIMP freeze-out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74WIMP ”miracle” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76νMSM: all masses below electroweak scale . . . . . . . . . . . . . . . . . . . . . . 78νMSM: all masses below electroweak scale . . . . . . . . . . . . . . . . . . . . . . 79. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Decaying DM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Properties of decaying DM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Decay signal from MW-sized galaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Annihilation signal from MW-sized galaxy . . . . . . . . . . . . . . . . . . . . . . . . . 86Decay vs. annihilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Primordial properties of super-WIMPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Subhalo mass function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91How to probe primordial velocities? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92Lyman-α forest and cosmic web . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93The Lyman-α method includes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Lyman-α forest and warm DM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Halo (sub)structure in CDM+WDM universe . . . . . . . . . . . . . . . . . . . . . . 96


TOC

Halo (sub)structure in CDM universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Halo (sub)structure in CDM+WDM universe . . . . . . . . . . . . . . . . . . . . . . 98Window of parameters of sterile neutrino DM . . . . . . . . . . . . . . . . . . . . . 99Window of parameters of sterile neutrino DM . . . . . . . . . . . . . . . . . . . . 100Window of parameters of sterile neutrino DM . . . . . . . . . . . . . . . . . . . . 101Window of parameters of sterile neutrino DM . . . . . . . . . . . . . . . . . . . . 102Window of parameters of sterile neutrino DM . . . . . . . . . . . . . . . . . . . . 103Baryon asymmetry of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104Baryon asymmetry in the present universe . . . . . . . . . . . . . . . . . . . . . . 105Antiprotons in the universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106Positrons in the universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Baryon asymmetry of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108Matter-antimatter asymmetry in particle physics . . . . . . . . . . . . . . . . . . . . . . . . . 109Matter-antimatter puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Thermal history of baryon asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Sakharov conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Baryon number non-conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113C- and CP-non-conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114


TOC

Deviation from thermal equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Phase transitions in the early Universe . . . . . . . . . . . . . . . . . . . . . . . . . . 116Phase transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Phase transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1181st order phase transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1192nd order phase transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Search for decaying DM: main challenges . . . . . . . . . . . . . . . . . . . . . . . 121DM in Andromeda galaxy (2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Mass-to-light ratio in Andromeda galaxy? . . . . . . . . . . . . . . . . . . . . . . . 123DM in Andromeda galaxy (2010) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124DM distribution in individual objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Universal properties of DM distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 126Constant surface density? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127An evidence in favor of MOND? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Observations vs. simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Observations vs. simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Universal properties of DM distributions? . . . . . . . . . . . . . . . . . . . . . . . .131Comparing DM density profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132


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Observations vs. simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Universal scaling of DM column density . . . . . . . . . . . . . . . . . . . . . . . . . 134Universal scaling of DM column density . . . . . . . . . . . . . . . . . . . . . . . . . 135Independent determination of mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136Independent determination of mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137Qualitative understanding? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .138DM column density in infall model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139Qualitative understanding? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .140Restrictions on modifications of gravity . . . . . . . . . . . . . . . . . . . . . . . . . . 141Direct astrophysical detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142Restrictions on sterile neutrino DM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Restrictions on life-time of decaying DM . . . . . . . . . . . . . . . . . . . . . . . . . 144New mission: EDGE/XENIA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

Qualitative understanding? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .147DM column density in infall model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Example: Lyman-α forest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Observational data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .150


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Parameters of Aquarius simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153CMB anisotropies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154CMB anisotropy map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155CMB anisotropies (cont.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .156WMAP + small scale experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157What (how) can we learn from CMB? . . . . . . . . . . . . . . . . . . . . . . . . . . . .158. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Evolution of structures? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160Structure formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161Analytical model: spherical collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162Analytical model: secondary infall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Secondary infall model: phase-space . . . . . . . . . . . . . . . . . . . . . . . . . . . 164Turn-around radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165Cosmic web . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166Jeans instability I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Jeans instability II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168


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Jeans instability in expanding Universe . . . . . . . . . . . . . . . . . . . . . . . . . . 169Jeans instability in expanding Universe . . . . . . . . . . . . . . . . . . . . . . . . . . 170Real CMB physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171Growth of perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172Cosmological parameters and CMB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Large scale structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .174Large scale structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175Large scale structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176Free-streaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177Free-streaming (numbers) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178Thermal relics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179


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