Primordial Gravity Waves and Weak Lensing

TL;DR

It is found that the expected signal from inflation is small, peaking on the largest scales at l(l+1)C(l)/2pi<10(-11) at l=2 and falling rapidly thereafter.

Abstract

Inflation produces a primordial spectrum of gravity waves in addition to the density perturbations which seed structure formation. We compute the signature of these gravity waves in the large scale shear field. In particular, the shear can be divided into a gradient mode (G or E) and a curl mode (C or B). The former is produced by both density perturbations and gravity waves, while the latter is produced only by gravity waves, so the observations of a non-zero curl mode could be seen as evidence for inflation. We find that the expected signal from inflation is small, peaking on the largest scales at $l(l+1)C_l/2π< 10^{-11}$ at $l=2$ and falling rapidly there after. Even for an all-sky deep survey, this signal would be below noise at all multipoles. Part of the reason for the smallness of the signal is a cancellation on large scales of the standard line-of-sight effect and the effect of ``metric shear.''

Figures (1)

• Figure 1: Expected signal in an all-sky survey in the curl mode in a model with $\Omega_m=0.3,\Omega_\Lambda=0.7$ with (solid) and without (dashed) the metric shear term of Eq. (15). The Hubble rate during inflation which determines the amplitude of the gravity wave power spectrum has been set to $2\times 10^{14}$ GeV. The noise estimate here assumes an all-sky survey with $1.5\times 10^{10}$ galaxies and the variance of the intrinsic shear equal to $0.1$. Background galaxies are all assumed to be at fixed redshift $3$.