Primordial Gravity Waves and Weak Lensing

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. The shear can be divided into a gradient mode ($G$ or $E$) and a curl mode ($C$ or $B$). The latter is produced only by gravity waves, so the observations of a nonzero 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 $l(l+1)C_l/2\pi <{10}^{-11}$ at $l=2$ and falling rapidly thereafter. Even for an all-sky deep survey, this signal would be below noise at all multipoles.

Figure 1

Expected variance of the shear 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 $2\times {10}^{14}\mathrm{G}\mathrm{e}\mathrm{V}$. 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 $3$.