Post-Newtonian Sachs-Wolfe Effect

Abstract

Deviations from the Friedmann-Robertson-Walker (FRW) cosmological model in the form of density inhomogeneities induce observational effects on the light propagating through these fluctuations. Using a rigorously parametrized metric whose pseudo-Newtonian potential is related to (possibly nonlinear) density inhomogeneities through a relativistic Green function, the behavior of radiation propagating through this approximation to our universe is investigated, without relying on any spatial averaging or late time, short perturbation wavelength Newtonian limit. In certain regimes the energy shift of a photon due to density fluctuations, the Sachs-Wolfe effect, is found to deviate significantly from the linearized relativity (Poisson-Newton) result, but the corresponding cosmic microwave background temperature fluctuations are still below $10^{-6}$ on small scales. On large scales this can be treated as an effective transfer function for the density power spectrum, altering the scaling of the amplitudes of large versus small scale power.