Dark Matter and Dark Energy components
chapter 7
Lecture 4
See also Dark Matter awareness week December 2010
http://www.sissa.it/ap/dmg/index.html
The early universe chapters 5 to 8
Particle Astrophysics , D. Perkins, 2nd edition, Oxford
5. The expanding universe 6. Nucleosynthesis and baryogenesis 7. Dark matter and dark energy components 8. Development of structure in early universe
Slides + book http://w3.iihe.ac.be/~cdeclerc/astroparticles
Overview
• Part 1: Observation of dark matter as gravitational effects – Rotation curves galaxies, mass/light ratios in galaxies
– Velocities of galaxies in clusters
– Gravitational lensing
– Bullet cluster
• Part 2: Nature of the dark matter : – Baryons and MACHO’s
– Standard neutrinos
– Axions
• Part 3: Weakly Interacting Massive Particles (WIMPs)
• Part 4: Experimental WIMP searches
• Part 5: Dark energy
2012-13 Dark Matter - Dark Energy 3
Previously – ΛCDM model
• Universe is flat k=0
• Dynamics given by Friedman equation
• Size of universe at given time
and today , t0
• Closure parameter relates density to critical density • Energy density evolves with time, and so does H
2012-13 Dark Matter - Dark Energy 4
2
2 8
3
NR t G
R ttH t totρ
0
01 0R t
z z tR t
c
tt
t
2 3 4 22
0 0 01 1 1r kH t H z t z t z0 0m ΛΩ t Ω t
Ωk=0
tot mat rad
Energy budget of universe today
2012-13 Dark Matter - Dark Energy 5
luminous 1%
dark baryonic
4%
Neutrino HDM <1% cold dark
matter 18%
dark energy
76%
• Today only 5% of the matter-energy consists of known particles
• 18% is Cold Dark Matter = new type of particles
• 76% is completely unknown 510
0.24
rad
matter
2 3 42
0 0 0 01 1m rH t H t z t z t
Previous lecture : Dark Matter
• Observation of dark matter as gravitational effects
• Nature of dark matter particles is still inknown
– Baryons
– MACHOs = Massive Compact Halo Objects
– Neutrinos
– Axions
– WIMPs = Weakly Interacting Massive Particles
• Identifying dark matter : direct and indirect detection experiments
2012-13 Dark Matter - Dark Energy 6
Ωm
Where should we look?
• Search for WIMPs in the Milky Way halo
Indirect detection: expect WIMPs from the halo to annihilate with each other to known particles
Direct detection: expect WIMPs from the halo to interact in a detector on Earth
2012-13 Dark Matter - Dark Energy 7
Dark matter halo
Luminous disk
Solar system
© ESO
PART 4: WIMP DETECTION
Identify the nature of dark matter with experiments
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DIRECT DETECTION EXPERIMENTS
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Principle of direct detection
• Earth moves in WIMP ‘wind’ from halo
• Elastic collision of WIMP with nucleus in detector
• recoil energy
• Velocity of WIMPs ~ velocity of galactic objects
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N N
2
Rec 1 cos 50N
E keVm
2v µ
N
N
m m
m mµ
1 3~ 270 ~ 10km s cχv
Cross section and event rates
• Event rate depends on density of WIMPs in solar system
• Rate depends on scattering cross section – present upper limit
2012-13 Dark Matter - Dark Energy 11
Rm
N χpσ
3~ 0.3GeV cm
DM
Den
sity
(G
eV c
m-3
)
Distance from centre (kpc)
Rate depends on number N of nuclei in target
44 2 810 10cm pbσ χp Weak interactions!
• low rate
large detector
• very small signal
low threshold
• large background :
protect against cosmic rays, radioactivity, …
2012-13 Dark Matter - Dark Energy 12
Direct detection challenges
pRM
N
Annual modulation
• Annual modulations due to movement of solar system in galactic WIMP halo – 30% effect
• Observed by DAMA/LIBRA – not confirmed by other experiments
2012-13 Dark Matter - Dark Energy 13
pRM
N
1~ 270v km s
Against the wind in June higher rate
In direction of the wind in December Lower rate
From event rate to cross section
2012-13 Dark Matter - Dark Energy 14
R NM
χpσ
Other experiments see no signal and put upper limits on the cross section
Some experiments claim to see a signal at this mass and with this cross section
Expected cross sections for models with supersymmetry
INDIRECT DETECTION EXPERIMENTS
2012-13 Dark Matter - Dark Energy 15
Indirect detection of WIMPs • Search for signals of annihilation of WIMPs in the Milky Way halo
• accumulation near galactic centre or in heavy objects like the Sun or Earth due to gravitational attraction
• Detect the produced antiparticles, gamma rays, neutrinos
2012-13 Dark Matter - Dark Energy 16
, , ,..
, ,
ll e
W Z H
neutrinos from WIMP annihilations : IceCube
• Neutrinos from WIMP annihilations in the Sun
• Neutrinos from WIMP annihilations in galactic halo, galactic centre, dwarf spheroidal galaxies
• Neutrinos from WIMP annihilations in the centre of the Earth
2012-13 17 Dark Matter - Dark Energy
WIMPs accumulated in the Sun
2012-13 Dark Matter - Dark Energy 18
Detector
μ
ν interaction
, ,...qq ll
1. WIMPs are captured 3 2SUNC
v m
χNσ
2. WIMPs annihilate
1
2ANN SUNC
Capture rate
Annihilation rate
19
Search for GeV-TeV neutrinos from Sun
A few 100’000 atmospheric neutrinos per year from northern hemisphere
Max. a few neutrinos per year from WIMPs in the Sun
signal
~1011 atmospheric muons per year from southern hemisphere
BG
BG
2012-13 Dark Matter - Dark Energy
No excess above known backgrdound
2012-13 Dark Matter - Dark Energy 20
Data Background
• No significant signal found
• Rate is compatible with atmospheric background
• Set upper limit on possible neutrino flux and annihilation rate
ψ(deg)
Nu
mb
er o
f ev
ents
Sign
al?
Combining direct and IceCube searches
2012-13 Dark Matter - Dark Energy 21
IceCube
W W
2
SD p cm
A selection of SuperSymmetry models
~ ~Ann SUNC χNσ
Overview
• Part 1: Observation of dark matter as gravitational effects
– Rotation curves galaxies, mass/light ratios in galaxies
– Velocities of galaxies in clusters
– Gravitational lensing
– Bullet cluster
• Part 2: Nature of the dark matter :
– Baryons and MACHO’s
– Standard neutrinos
– Axions
• Part 3: Weakly Interacting Massive Particles (WIMPs)
• Part 4: Experimental WIMP searches
• Part 5: Dark energy
2012-13 Dark Matter - Dark Energy 22
Part 5: Dark Energy
Observations
The nature of Dark Energy ΩΛ
Energy budget of universe today
2012-13 Dark Matter - Dark Energy 24
luminous 1%
dark baryonic
4%
Neutrino HDM <1% cold dark
matter 18%
dark energy
76%
• Today only 5% of the matter-energy consists of known particles
• 18% is Cold Dark Matter = new type of particles
• 76% is completely unknown 510
0.24
rad
matter
2 3 42
0 0 0 01 1m rH t H t z t z t
OBSERVATIONS
SNIa surveys
Link to cosmological parameters
2012-13 Dark Matter - Dark Energy 25
2012-13 Dark Matter - Dark Energy 26
Nobel Prize in Physics 2011
SNIa as standard candles (see lecture 1)
• Supernovae Ia are very bright - very distant SN can be observed
• All have roughly the same luminosity curve which allows to extract the absolute magnitude M
• → effective magnitudes yield luminosity distance
• Network of telescopes united in
– Supernova Cosmology Project SCP, (Perlmutter) up to z=1.4 – have now data from 500 SN (http://supernova.lbl.gov/)
– High-z SN search HZSNS (Schmidt & Riess, in 1990’s) 2012-13 Dark Matter - Dark Energy 27
10
2.5log
5log 251Mpc
M L cst
z M LD
m
Luminosity distance vs redshift - 1
• SN at redshift z emits light at time tE – is observed at time t0
• Light observed today travelled during time (t0 - tE )
• distance travelled depends on history of expansion
• Proper distance DH from SN to Earth (lecture 1, horizon
distance)
• For flat universe (k=0) with negligible radiation content
2012-13 Dark Matter - Dark Energy 28
32 2 2
0 0 0( ) 1mH z H t H t z t
0
0
EE
t
t
dct R t
R t
tHD
1
dz
zd
Ht
Luminosity distance vs redshift - 2
• Luminosity distance
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300 00 0
12
1
z z
m
cdz c dz
Ht z t
HH z
D z
1 z HD zLD z
Luminosity distance DL vs redshift z
• Neglect radiation at low z – different examples
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normalise to empty universe
• normalise measurements to empty universe
• Deceleration parameter is zero – universe is ‘coasting’
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0 0 01, 0, 0k mt t t
2
2
R R Rq t
R R R
R
02
mr
tq t t t
20 00
12
1 12
1
z
L
c dz c zD empty z z
H Hz
R = 0
Hubble plot with high z SNIa
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Empty universe: Ωm= Ωr=0 Ωk=1 No acceleration no deceleration
Vacuum dominated & flat
Matter dominated & flat
Log
DL
(Mp
c)
Redshift Z past now
Influence of cosmological parameters
• best fit
• Empty universe
2012-13 Dark Matter - Dark Energy 33
Difference between measured logDL vs z and expected logDL vs z for empty universe
best fit
Empty universe
measurements
Measurements up to z=1.7
• Best fit
2012-13 Dark Matter - Dark Energy 34
0 00.27 0.73m t t
log logL LD measured D empty
…. empty --- Best fit
Δ(m
-M)=Δ
DL
z
q(t)<0 acceleration q(t)>0 deceleration
past present
SN observations show acceleration
• Early universe : universe dominated by matter decelerates due to gravitational collapse :
• Recently : universe dominated by vacuum energy accelerates
• Acceleration = zero around z=0.5 when
• → Switch from deceleration (matter dominated) to acceleration (dark energy dominated)
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2
mr
tq t t t
0 0mq t t R
0 0q t t R
2
mr
tt t
THE NATURE OF DARK ENERGY
Related to cosmological constant ?
problems
2012-13 Dark Matter - Dark Energy 36
Dark vacuum Energy
• Observed present-day acceleration means that Dark Energy generates a negative pressure
• Yields gravitational repulsion like vacuum energy
• Equation of state (see lecture 1)
• Fits to SNIa data yield that w is compatible with vacuum energy
2012-13 Dark Matter - Dark Energy 37
2
vac
S
EP c cst
V2
Pw
c
0.85 at 95% . .w C L
Related to cosmological constant Λ
• In ΛCDM – ΩΛ is constant and related to Einsteins cosmological constant
• If Universe contains constant vacuum energy density related to Λ then we set
• In very early Universe there was only vacuum energy
• At Planck energy scale gravity becomes strong
• energy and length scales
• And expected energy density
2012-13 Dark Matter - Dark Energy 38
8 vacG
15 2
2 191.2 10def
PL
cM c GeV
G
351.6 10DEF
PL
PL
L mM c
22 123 3
exp 310PL
vac
PL
M cc GeV m
L
Cosmological constant problem
• Today vacuum energy density is of order of critical density
• Discrepancy of 100 orders of magnitude !!!
• Did vacuum energy evolve with time?
• There is no explanation yet
• need high statistics data :
– Dark Energy Survey – start 2011 (http://www.darkenergysurvey.org/)
– WFIRST mission of NASA – launch 2020 (http://wfirst.gsfc.nasa.gov/ )
– ESA EUCLID mission – launch 2015-20 (http://www.esa.int )
2012-13 Dark Matter - Dark Energy 39
2 2 30.76 5vac critobs
c c GeV m 2 123 3
exp10vacc GeV m
Alternatives
• Quintessence – 5th force : acceleration is due to potential energy of a dynamical field
• Vacuum energy density varies with time
• Mechanism analogue to inflation
in early universe
• Maybe general relativity works differently at large distances
2012-13 Dark Matter - Dark Energy 40
2
Pw t
c
113
w t
Summary
• Observations of SNIa emission show that the universe presently accelerates
• This can be explained by a constant dark vacuum energy contribution which dominates today
• In the ΛCDM model the dark energy is related to the cosmological constant introduced by Einstein
• There is yet no satisfactory explanation for the observed magnitude of the dark energy
2012-13 Dark Matter - Dark Energy 41
Overview
• Part 1: Observation of dark matter as gravitational effects – Rotation curves galaxies, mass/light ratios in galaxies
– Velocities of galaxies in clusters
– Gravitational lensing
– Bullet cluster
• Part 2: Nature of the dark matter : – Baryons and MACHO’s
– Standard neutrinos
– Axions
• Part 3: Weakly Interacting Massive Particles (WIMPs)
• Part 4: Experimental WIMP searches
• Part 5: Dark energy
2012-13 Dark Matter - Dark Energy 42