Tensor Perturbations in Inflationary Models as a Probe of Cosmology

TL;DR

Because tensor perturbations give rise to the anisotropy of the cosmic background radiation (CBR) solely through the Sachs-Wolfe effect, the transfer function is provided, and it is shown that it is unlikely that the stochastic background of gravity waves can be detected directly in the foreseeable future.

Abstract

In principle, the tensor metric (gravity-wave) perturbations that arise in inflationary models can, beyond probing the underlying inflationary model, provide information about the Universe: ionization history, presence of a cosmological constant, and epoch of matter-radiation equality. Because tensor perturbations give rise to anisotropy of the cosmic background radiation (CBR) solely through the Sachs-Wolfe effect we are able to calculate analytically the variance of the multipole moments of this part of the CBR temperature anisotropy. In so doing, we carefully take account of the contribution of tensor perturbations that entered the Hubble radius during both the matter-dominated and radiation-dominated epoch by means of a transfer function. The striking feature in the spectrum of multipole amplitudes is a dramatic fall off for $l\ga \sqrt{1+\zl}$, where $\zl$ is the red shift of the last-scattering surface. ...