Cosmological Perturbation Theory to second order for curvature, density, and gravity waves on FRW background; and the WMAP results of inhomogeneity and clustering in the early universe

TL;DR

This paper develops second order cosmological perturbation theory for curvature, density, and gravity waves on FRW backgrounds, and relates these to WMAP observations of early universe inhomogeneity and clustering.

Contribution

It provides exact second order perturbation equations for FRW cosmology and applies suitable approximations to connect theoretical predictions with WMAP data.

Findings

Gravity waves couple nonlinearly, redistributing modes to higher 'l' values.

Second order perturbations relate curvature and density fluctuations.

WMAP data supports a deformed FRW spacetime with small inhomogeneities.

Abstract

The second order perturbation calculations for gravity wave and Einstein equation for space time and matter are presented for the FRW metric cosmological model. While exact equations are found, suitable approximations are made to obtain definite results. In the gravity wave case the small wavelength case allows nearly locally flat background for obtaining a fit to the WMAP data. In the density and curvature case the FRW background is retained for the length scale of WMAP. Clustering and inhomogeneity are understood. The gravity wave ripples from Big Bang couple nonlinearly and redistribute the modes to higher values of 'l' giving consistency with the WMAP results. The order by order consistency of Einstein equations relate the second order perturbations in the curvature and density and the wrinkles in spacetime caused by the gravity wave modes reorganize these distributions. The radiation data of WMAP gives the picture of a FRW spacetime deformed and wrinkled consistent with matter distribution to one hundred thousandths parts variation.