cosmic microwave background - indico
TRANSCRIPT
Cosmic Microwave Background
Vincent DesjacquesInstitute for Theoretical Physics
University of Zürich
CHIPP astroparticle meeting, EPFL, June 3rd , 2009
Thermal history of the Universe
Now
Physics of recombination:
In thermal equilibrium, for T<< mp , number densities are
Using ne=np , nB=np+nH, Saha's equation for ionized fraction xe=ne/nB reads
where B is the photontobaryon ratioTrec = 0.32 eV
Thompson scattering maintains photon temperature close to matter temperature.Decoupling occurs when T(Tdec)=H(Tdec).
Tdec=0.26 eV
Last scattering – visibility function
The visibility function g(z) is the probability that a CMB photon was last scatteredin the redshift interval [z, z+dz]
zdec~ 1088 Below zdec, the photon distribution f
evolves according to the Liouville equation
T(0) = T
(zdec)/(1+zdec)
~ 2.5 104 eV ~ 2.7 K
(1965)
COBE/FIRAS (1990) : Nearly perfect blackbody at T0=2.73 K
Mather et al (1990)
COBE/DMR (1992) : temperature anisotropies T/T0 ~ 105
SachsWolfe Effect (1967): T/T0=/3
Cold spots = larger photon overdensity = stronger gravity
Smoot et al. (1992)
WMAP (2000 – present):
Hinshaw et al (2009)
CMB temperature anisotropies resolved down to ~ 13 arcmins
Foreground contaminationMeasure CMB anisotropies in several frequency channels to remove freefree, synchrotron dust microwave emissionfrom Milkyway + extragalactic sources
Hinshaw et al (2009)
Why are CMB anisotropies so useful ?
Baryontophoton ratio B
Sound speed and inertia of photonbaryon fluidMattertoradiation ratio m /
Dark matter abundance Neutrinos + other relativistic components
Angular diameter distance to Last Scattering Surface Position of acoustic peaks
Time dependence of gravitational potential Integrated SachsWolfe effect, Dark Energy
Optical depth cosmic reionization
Primordial power spectrum (scalar+tensor) Slowroll inflation gravity waves (CMB polarization)
Primordial nonGaussianity constraints on inflationary models
CMB temperature power spectrum
CMB temperature anisotropies are expanded in spherical harmonics
The CMB temperature power spectrum is the ensemble average
For Gaussian fluctuations, lm are Gaussian distributed and Cl
TT containthe full statistical information of the CMB temperature distribution
Fundamental limitation set by cosmic variance:
Measured ClTT
large scales small scales
>1o
SW plateaugrav. potential
6'<<1o
Acoustic peaksphotonbaryon fluid
<6'Damping
photon diffusion
Nolta et al (2009)
The physics of CMB temperature anisotropies
Solve a coupled set of relativistic Boltzmann equations
and the Einstein equations
to first order in perturbations around a FRW Universe with metric
and stressenergy tensor
Cosmological perturbation theory
A general perturbation to the FRW metric may be represented as
while for the stressenergy tensor one may choose
i) Go to Fourier space. Translation invariance of the linearized equations of motion implies that different Fourier modes do not interact.ii) Decompose the perturbations into scalar (S), vector (V) and tensor (T) components, each of which evolves independently at first order.iii) Choose a gauge (coordinates) according to the problem considered (i.e. evolution of CMB, inflationary, neutrinos fluctuations etc.)
Photon propagation
The distribution function for photons of energy E and propagation direction n is a perturbed BlackBody spectrum,
In the presence of gravity and collisions, the evolution of =T/T0 in the Newtonian gauge is governed by
photons scatteredout of the beam
photons scatteredinto the beam
e are not at rest w.r.t.cosmic frame
Multiplying by exp() and integrating over the conformal time,
In the instantaneous recombination limit,
acoustic peaks+ SW effect Integrated SachsWolfe (ISW)Doppler
Photonbaryon fluid equations
In the Newtonian Gauge, the equations for the scalar modes of a relativistic fluid of photons and baryons are
CONTINUITY
EULER
EINSTEIN (POISSON)
R=3B/4~B is the baryonphoton momentum density ratio, and
is the
photon anisotropic stress perturbation
Tight coupling approximation
When the scattering is rapid compared to the travel time across a wavelength,
The baryon velocity can be eliminated and the eqs. for photons combine into
Below the sound horizon
photon pressure resits gravitational compression and sets up acoustic oscillations.Neglecting the time variation of R, the effective temperature evolves as
The initial conditions (ICs) determine A and B: B=0 (adiabatic)A=0 (isocurvature)
Peebles & Yu (1970), Hu & Sugiyama (1995)
Photon diffusion
Photons have a finite mean free path > the coupling baryonphoton is not perfectat small scales where photon diffusion erases temperature differences and causesanisotropic stress (viscosity).
Free streaming transfers power to higher multipoles so, in principle, one should solve the full Boltzmann hierarchy
First peak at lpeak≈200 + cosine series > inflation !
Acoustic oscillations are frozen in the CMB at decoupling
com
pres
sion
pea
k
expa
nsio
n pe
akDoppler peaks are
out of phase
ISW, SW
CMB polarization
Thomson scattering of radiation with a temperature quadrupole anisotropygenerates linear polarization at recombination
COLD
HOT
linear polarization
Intensity matrix:
Stokes parameters:
Theory: CMB anisotropies polarized at 510% level
Bond & Efstathiou (1984)
Dunkley et al (2009)
CMB Synchrotron Dust emission
Q
U
WMAP: CMB anisotropies indeed are polarized !
constrain optical depth to reionization
Dunkley et al (2009)
CMB Synchrotron Dust emission
Q
U
Emode and Bmode decomposition
The Stokes parameters Q,U transform as a spin2 field under rotation
hence may be expanded in terms of tensor (spin2) spherical harmonics
It is convenient to introduce the spin0 (rotationally invariant) E and Bmodes
where
Seljak & Zaldarriaga (1997), Kamionkowski et al (1997)
Polarization pattern = Emodes (curlfree) + Bmodes (divergencefree)
Bmode = smoking gun of inflation
scalar (density) perturbations create only Emodes vector (vorticity) perturbations create mainly Bmodes tensor (gravity waves) pertur bations create both E and B modes
In a parityconserving Universe, there are four observable angular powerspectra commonly named TT, TE, EE and BB
WMAP 5year ClTE , Cl
EE
ClBB consistent with zero
inflation
Emode detected at high level of significance !
How do we compute CMB power spectra ?
Use the lineofsight technique, i.e. write down an integral solution to the Boltzmannequation. This is the method implemented in CMBFast.
Seljak & Zaldarriaga (1996)
SCALAR
TENSOR
The transfer functions are
Primordial perturbations
A convenient phenomenological parametrization of the power spectrum of primordial scalar (density) and tensor (gravity waves) perturbations is
CMB polarization measurements are sensitive to the tensortoscalar ratio
ns, s, nt, As and r can be related to the modeldependent shape of the inflatonpotential
Scalar T
Scalar E
Tensor T
Tensor E
Tensor B
WMAP 5year constraints on cosmological parameters
Komatsu et al (2009)
Scaleinvariant (HZ) spectrum excluded at 3 (r=0) !
Dark Energy / Cosmological Constant
CMB data alone cannot constrain the Dark Energy equation of state. Combine with largescale structure data to break degeneracies.
Komatsu et al (2009)
Primordial nonGaussianity
Minkowski functionalsWMAP 5year measured Minkowskifunctionals and threepoint functionof CMB temperature fluctuations.
Planck satellite
lauchned on 14/05/09
highly sensitive bolometer detectors cooled down to 0.1K high angular resolution (l ~ 1500) map of the whole sky in 9 frequency channels > CMB anisotropies, SZ, extragalactic sources etc.
CMB secondary anisotropies (SZ, lensing etc.) tighten constraints on cosmological parameters study ionization history of the Universe probe the dynamic of the inflationary era test fundamental physics, e.g. braneworld or preBig Bang cosmologies
Summary
A flat, nearly scaleinvariant CDM model fits the CMB temperature and polarization data very well.The measurements are consistent with singlefield slow roll inflation .
Future CMB experiments (Planck, CMBPol):
improve Bmode/nonGaussianity measurement (detection/upper limit)
constrain inflation !