Gravity of Cosmological Perturbations in the CMB

Abstract

First, we establish which measures of large-scale perturbations are least afflicted by gauge artifacts and directly map the apparent evolution of inhomogeneities to local interactions of cosmological species. Considering nonlinear and linear perturbations of phase-space distribution, radiation intensity and arbitrary species' density, we require that: (i) the dynamics of perturbations defined by these measures is determined by observables within the local Hubble volume; (ii) the measures are practically applicable on microscopic scales and in an unperturbed geometry retain their microscopic meaning on all scales. We prove that all measures of linear overdensity that satisfy (i) and (ii) coincide in the superhorizon limit. Their dynamical equations are simpler than the traditional ones, have a nonsingular superhorizon limit and explicit Cauchy form. Then we show that, contrary to the popular view, the perturbations of the cosmic microwave background (CMB) in the radiation era are not resonantly boosted self-gravitationally during horizon entry. (Consequently, the CMB signatures of uncoupled species which may be abundant in the radiation era, e.g. neutrinos or early quintessence, are mild; albeit non-degenerate and robust to cosmic variance.) On the other hand, dark matter perturbations in the matter era gravitationally suppress large-angle CMB anisotropy by an order of magnitude stronger than presently believed. If cold dark matter were the only dominant component then, for adiabatic perturbations, the CMB temperature power spectrum C_l would be suppressed 25-fold.