The mildly nonlinear imprint of structure on the CMB

Abstract

I outline some nonperturbative relativistic effects that arise from gravitational corrections to the Boltzmann equations. These may be important for the study of CMB temperature anisotropies, particularly their interpretation. These terms are not included in the canonical treatment as they arise from the exact equations. Here a weakly nonlinear investigation of these effects is defined and investigated with an emphasis on a Rees-Sciama sourced effect -- the imprint of structure evolution on the CMB. It is shown that gravitational nonlinearity in the weakly nonlinear extension of almost-FLRW temperature anisotropies leads to cancellation on small-scales when threading in the Newtonian frame. In the general frame this cancellation does not occur. In the context of a flat almost-FLRW CDM model I provide a heuristic argument for a nonperturbative small scale correction, due to the Rees-Sciama effect, of not more than $ΔT/T \sim 10^{-6}-10^{-5}$ near $\ell \sim 100 - 300$. The effect of mild gravitational nonlinearity could be more sophisticated than previously expected.