CMB spectral distortions from small-scale isocurvature fluctuations

The damping of primordial perturbations at small scales gives rise to distortions of the cosmic microwave background (CMB). Here, the dependence of the distortion on the different types of cosmological initial conditions is explored, covering adiabatic, baryon/cold dark matter isocurvature, neutrino density/velocity isocurvature modes and some mixtures. The radiation transfer functions for each mode are determined and then used to compute the dissipative heating rates and spectral distortion signatures, utilizing both analytic estimates and numerical results from the thermalization code CosmoTherm. Along the way, the early-time super-horizon behavior for the resulting fluid modes is derived in conformal Newtonian gauge, and tight-coupling transfer function approximations are given. CMB spectral distortions caused by different perturbation modes can be estimated using simple k-space window functions which are provided here. Neutrinos carry away some fraction of the primordial perturbation power, introducing an overall efficiency factor that depends on the perturbation type. It is shown that future measurements of the CMB frequency spectrum have the potential to probe different perturbation modes at very small scales (corresponding to wavenumbers 1 Mpc^{-1} < k < few x 10^4 Mpc^{-1}). These constraints are complementary to those obtained at large scales and hence provide an exciting new window to early-universe physics.