Jens Chluba, Rishi Khatri, Rashid A. Sunyaev
Silk damping of primordial small scale perturbations in the photon-baryon
fluid due to diffusion of photons inevitably creates spectral distortions in
the CMB. With the proposed CMB experiment PIXIE it might become possible to
measure these distortions and thereby constrain the primordial power spectrum
at comoving wavenumbers 50 Mpc^{-1} < k < 10^4 Mpc^{-1}. Since primordial
fluctuations on these scales are completely erased by Silk damping, these
distortions may provide the only way to shed light on otherwise unobservable
aspects of inflationary physics. A consistent treatment of the primordial
dissipation problem requires going to second order in perturbation theory,
while thermalization of these distortions necessitates consideration of second
order in Compton scattering energy transfer. Here we give a full 2x2 treatment
for creation and evolution of spectral distortions due to the acoustic
dissipation process, consistently including the effect of polarization and
photon mixing in the free streaming regime. We show that 1/3 of the total
energy (9/4 larger than previous estimate) stored in small scale temperature
perturbations imprints observable spectral distortions, while the remaining 2/3
only raise the average CMB temperature, an effect that is unobservable. At high
redshift dissipation is mainly mediated through the quadrupole anisotropies,
while after recombination peculiar motions are most important. During
recombination the damping of the higher multipoles is also significant. We
compute the average distortion for several examples using CosmoTherm, analyzing
their dependence on parameters of the primordial power spectrum. For one of the
best fit WMAP7 cosmologies, with n_S=1.027 and n_run=-0.034, the cooling of
baryonic matter practically compensates the heating from acoustic dissipation
in the mu-era. (abridged)
View original:
http://arxiv.org/abs/1202.0057
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