Large-Scale Structure with Gravitational Waves II: Shear

Abstract

The B-(curl-)mode of the correlation of galaxy ellipticities (shear) can be used to detect a stochastic gravitational wave background, such as that predicted by inflation. In this paper, we derive the tensor mode contributions to shear from both gravitational lensing and intrinsic alignments, using the gauge-invariant, full-sky results of arXiv:1204.3625. We find that the intrinsic alignment contribution, calculated using the linear alignment model, is larger than the lensing contribution by an order of magnitude or more, if the alignment strength for tensor modes is of the same order as for scalar modes. This contribution also extends to higher multipoles. These results make the prospects for probing tensor modes using galaxy surveys less pessimistic than previously thought, though still very challenging.

Figures (7)

• Figure 1: Lensing (projection) contributions to the observed angular power spectrum of the $E$-mode component of the shear from tensor modes, separated into terms $\propto \hat{Q}_1$ (observer and FNC terms), $\propto \hat{Q}_2$ and $\propto \hat{Q}_3$ respectively. Note that power spectra are multiplied by $l^6$. We have assumed a sharp source redshift of $\tilde{z} = 2$.
• Figure 2:
• Figure 3: Angular power spectrum of the observed $E$-component of the shear from lensing and intrinsic alignment affects, as well as the total power spectrum. We assumed $C_1\rho_{\rm cr 0} = 0.12$ (following the results of BlazekEtal), and a Gaussian distribution of source redshifts centered at $\tilde{z} = 2$ with RMS width of $\Delta z = 0.03(1+\tilde{z})$.
• Figure 4: Same as Fig. \ref{['fig:Cl_IAE']}, but for $B$-modes.
• Figure 5: Dependence of the lensing and intrinsic alignment contributions to the $B$-mode shear power spectrum on the source redshift $\tilde{z}$. We have assumed a Gaussian redshift distribution centered at $\tilde{z} = 5$, 2, 1 (from top to bottom), and RMS width $\Delta z = 0.03 (1+\tilde{z})$. The black dotted line near the top of the figure shows the $1\sigma$ error on the shear power spectrum per multipole induced by shape noise [Eq. (\ref{['eq:Clshape']})], for a survey with $\bar{n} = 100\:{\rm arcmin}^{-2}$, $\sigma_e = 0.3$, and $f_{\rm sky} = 0.5$.