Second-order power spectra of CMB anisotropies due to primordial random perturbations in flat cosmological models

TL;DR

This paper investigates second-order effects on CMB anisotropies caused by primordial perturbations in flat cosmological models, revealing that these effects can dominate at early stages and are detectable with future observations.

Contribution

It derives the second-order power spectra of CMB anisotropies using relativistic perturbation theory and two-point correlations, highlighting the significance of second-order effects.

Findings

Second-order power spectra can surpass first-order spectra at early times.

Second-order integrated Sachs-Wolfe effect may dominate over first-order.

Future precise observations could measure these second-order effects.

Abstract

Second-order power spectra of Cosmic Microwave Background (CMB) anisotropies due to random primordial perturbations at the matter dominant stage are studied, based on the relativistic second-order theory of perturbations in flat cosmological models and on the second-order formula of CMB anisotropies derived by Mollerach and Matarrese. So far the second-order integrated Sachs-Wolfe effect has been analyzed using the three-point correlation or bispectrum. In this paper we derive the second-order term of power spectra given using the two-point correlation of temperature fluctuations. The second-order density perturbations are small, compared with the first-order ones. The second-order power spectra of CMB anisotropies, however, are not small at all, compared with the first-order power spectra, because at the early stage the first-order integrated Sachs-Wolfe effect is very small and the second-order integrated Sachs-Wolfe effect may be dominant over the first-order ones. So their characteristic behaviors may be measured through the future precise observation and bring useful informations on the structure and evolution of our universe in the future.