Cosmologia Osservativa

Lezione 26/5/2015

The Cosmic Microwave Background

Discovered By Penzias and Wilson in1965.

It is an image of the universe at thetime of recombination (near baryon-photons decoupling), when theuniverse was just a few thousand yearsold (z~1000).

The CMB frequency spectrumis a perfect blackbody at T=2.73 K:this is an outstanding confirmationof the hot big bang model.

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Uniform…

First Anisotropy we see is a Dipole anisotropy: Implies solar-system barycenter has velocity v/c~0.00123 relative to ‘rest-frame’ of CMB.

The Microwave Sky

COBE (circa 1995) @90GHz

If we remove the Dipole anisotropyand the Galactic emission, we see anisotropies at the levelof (ΔT/T) rms~ 20 μK (smoothed on~7° scale).These anisotropies are theimprint left by primordial tiny density inhomogeneities(z~1000)..

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Best Full Sky Map of the CMB before Planck: WMAP satellite (2002-2010) (linear combination of 30,60 and 90 GHz channels)

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Planck 2013 CMB Map

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Comparison with COBE and WMAP

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Planck 2013 TT angular spectrum

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The CMB Angular Power Spectrum

R.m.s. of has power per decade in l:

We can extract 4 independent angularspectra from the CMB:

- Temperature- Cross Temperature Polarization- Polarization type E (density fluctuations)- Polarization type B (gravity waves)

Planck 2013 release is only temperature ps. 19

The gravitational effects of intervening matter bend the path of CMB light on its way from the early universe to the Planck telescope. This “gravitational lensing” distorts our image of the CMB

Gravitational Lensing

A simulated patch of CMB sky – before lensing

10º

Gravitational Lensing

A simulated patch of CMB sky – after lensing

10º

Gravitational Lensing

Planck dark matter distribution throught CMB lensing

2º 0.2º

prediction based on the primary CMB fluctuations and the standard model

PLANCK LENSING POTENTIAL POWER SPECTRUMMeasured from the Trispectrum (4-point correlation)

It is a 25 sigma effect!!This spectrum helps in constraining parameters

Interpreting the Temperature angular power spectrum.

Some recent/old reviews:

Ted Bunn, arXiv:astro-ph/9607088

Arthur Kosowsky,  arXiv:astro-ph/9904102

Hannu Kurki-Suonio, http://arxiv.org/abs/1012.5204

Challinor and Peiris, AIP Conf.Proc.1132:86-140, 2009, arXiv:0903.5158

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CMB Anisotropy: BASICS

• Friedmann Flat Universe with 5 components: Baryons, Cold Dark Matter (w=0, always), Photons, Massless Neutrinos, Cosmological Constant.

• Linear Perturbation. Newtonian Gauge. Scalar modes only.

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• Perturbation Variables:

CMB Anisotropy: BASICS

Key point: we work in Fourier space :

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CMB Anisotropy: BASICS

CDM:

Baryons:

Photons:

Neutrinos:

Their evolution is governed by a nasty set of coupled partial differential equations:

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Numerical Integration- Early Codes (1995) integrate the full set of equations (about 2000 for

each k mode, approx, 2 hours CPU time for obtaining one single spectrum).

COSMICS first public Boltzmann code http://arxiv.org/abs/astro-ph/9506070.

- Major breakthrough with line of sight integration method with CMBFAST (Seljak&Zaldarriaga, 1996, http://arxiv.org/abs/astro-ph/9603033). (5 minutes of CPU time)

- Most supported and updated code at the moment CAMB (Challinor, Lasenby, Lewis), http://arxiv.org/abs/astro-ph/9911177 (Faster than CMBFAST).

- Both on-line versions of CAMB and CMBFAST available on LAMBDA website.

Suggested homework: read Seljak and Zaldarriga paper for the line of sight integration.

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CMB Anisotropy: BASICS

CDM:

Baryons:

Photons:

Neutrinos:

Their evolution is governed by a nasty set of coupled partial differential equations:

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First Pilar of the standard model of structure formation:

Standard model: Evolution of perturbations is passive and coherent.

Active and decoherent models of structure formation(i.e. topological defects see Albrecht et al, http://arxiv.org/abs/astro-ph/9505030):

Linear differentialoperator

Perturbation Variables

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Oscillations supporting evidence for passive and coherentscheme.

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Pen, Seljak, Turok, http://arxiv.org/abs/astro-ph/9704165Expansion of the defect source term in eigenvalues. Final spectrum does’nt show anyFeature or peak.

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Acoustic OscillationsIt is possible to show that the intrinsic temperature+gravity term has the solution (where and is the plasma sound speed) :

While the Doppler term (from the continuity equation) follows:

There is a simple physical picture underlying this result. The baryon-photon fluid wants to fall into the potential wells, but it is supported by radiation pressure. The balance between pressure and gravity sets up acoustic oscillations.

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Thermal History and Recombination

- Dominant element hydrogen recombines rapidly around z 1000.

– Prior to recombination, Thomson scattering efficient and mean free path short cf. expansion time

– Little chance of scattering after recombination ! photons free stream keeping imprint of conditions on last scattering surface

• Optical depth back to (conformal) time for Thomson scattering:

• The visibility function is the density probability of photon last scattering at time

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The CMB spectrum is essentially the quadrature sum of the two contributions.

Note the following:

a) When R=0 (no baryons) the quadrature sum gives:

i.e. no oscillations !!!Why does including the dynamical e ect of the baryons change the solution? The ffessential reason is that baryons contribute to the e ective mass of the photon-baryon fffluid, but not to the pressure.The e ect of the baryons, therefore, is to slow down the oscillations, and also to ffmake the fluid fall deeper into the potential wells.

CMB Anisotropies and Baryons

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Hu, Sugiyama, Silk, Nature 1997, astro-ph/9604166

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ProjectionA mode with wavelength λ will show up on an angular scale θ λ/R, ∼where R is the distance to the last-scattering surface, or in other words, a mode with wavenumber k shows up at multipoles l k.∼

The spherical Bessel function jl(x) peaks at x l, ∼so a single Fourier mode k does indeed contribute most of its power around multipole lk = kR, as expected. However, as the figure shows, jl does have significant power beyond the first peak, meaning that the power contributed by a Fourier mode “bleeds” to l-values different from lk.Moreover for an open universe (K is the curvature) :

l=30

l=60

l=90

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Projection

In Fourier space we have oscillationsWith frequency (or physical scale):

In Legendre space oscillations aresmeared and have a frequency thatDepends on the angular diameter distance at recombination.

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Planck 2013 TT angular spectrum

Constraints on LCDMPlanck improves theconstraints by a factor2-3 respect to WMAP9

Constraints on the Baryon Abundance from WMAP+SPT data

1.9% error !!

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Constraints on the Baryon Abundance from Planck data

1.3% error !!.

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Constraints on the Baryon Abundance from Planck data

1.3% error !!.

0.7% withTE EE

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Constraints on the CDM Abundance from WMAP+SPT data

23 sigmasEvidence forCDM !!

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Constraints on the CDM Abundance from Planck data

44 sigmasEvidence forCDM !!

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Constraints on the CDM Abundance from Planck data

80 sigmasEvidence forCDM Planck TT+TE+EE !!

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Constraints on Curvature from WMAP data

WMAP does NOT constrain Curvature !!

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Constraints on curvature from WMAP

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Constraints on curvature from Planck

Lensing in the TTspectrum helpsin breakingdegeneracy.

Geometrical degeneracySee, e.g. Efstathiou and Bond 1998Melchiorri and Griffiths, 2001

CMB Parameters• Baryon Density

• CDM Density

• Distance to the LSS, «Shift Parameter» :

decz

Km

Kzz

dzy

0 23 )1()1(

0,sinh

0,

0,sin

ky

ky

ky

y

yh

hR

k

M 2

2

2hb

2hCDM

Inflationary parameters

Sn

S k

kAkP

0

Inflationary parameters

3212 ,, PPnS

Baryonic Abundance

32122 ,, PPhB

Up to the 2nd peak n and the baryon density are degenerate.

200 400 600 800 1000 1200 1400

0,0

0,2

0,4

0,6

0,8

1,0

bh

2=0.034 n

s=1

bh

2=0.021 n

s=1

bh

2=0.021 n

s=0.7

l(l+

1)C

l

Multipole l

Degeneracy between spectral index and baryon density is seenin WMAP data.

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Degeneracy between spectral index and baryon density is alsopresent in Planck but is less evident ...

Planck 2015

During the slow-roll phase, the kinetic energy of the field is negligible and the potential is nearly constant:

This gives rise to a (quasi-) de Sitter phase:

The perturbations in the field are proportional to the value of the Hubble parameter at the time of horizon crossing:

Since V(f) is not actually constant, but slowly-varying, we expect a weak dependence of the amplitude of the perturbations on the wavenumber

If the perturbations were originated from the dynamics of a scalar field the spectrum should not be exactly scale invariant

H 2 8G3V ()

const.)(2

)(2

VV

k Hhc

2

2

2G

3V ()2

The spectral index as a «test» for inflation

• Inflation predicts but

• If this would provide an indication for the dynamical evolution as perturbation are being produced

1n

1n1n

How reionization is implemented when CMB anisotropies are

computed: simple «step» function !

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0

')'()'1(dz

zHz

xn eeT

The spectral index is almost completely degenerate with the optical depth.

Measuring large scale CMB polarization can break this degeneracy.