http://arxiv.org/abs/1412.4454
We describe a methodology to probe gravity with the CMB lensing convergence $\kappa$, specifically by measuring $E_G$, the ratio of the Laplacian of the gravitational scalar potential difference with the peculiar velocity divergence. Using $\kappa$ from CMB lensing as opposed to galaxy-galaxy lensing avoids intrinsic alignments while also lacking a hard limit on the lens redshift or significant uncertainties in the source plane. We model $E_G$ for general relativity and modified gravity, finding that $E_G$ for $f(R)$ gravity should be scale-dependent due to the scale-dependence of the growth rate $f$. Next, we construct an estimator for $E_G$ in terms of the lensing convergence-galaxy and galaxy angular power spectra, along with the RSD parameter $\beta$. We also forecast statistical errors of $E_G$ from the current Planck CMB lensing map and the CMASS and LOWZ spectroscopic galaxy samples measured from the BOSS survey, as well as BOSS spectroscopic quasars, from the SDSS Data Release 11. We expect this experimental configuration to detect $E_G$ at the level of 11$\sigma$ with CMASS/LOWZ galaxies alone and 13$\sigma$ when BOSS quasars are included. We also find that both upcoming spectroscopic and photometric surveys, each set combined with the final Planck lensing map, can measure precisely both the redshift- and scale-dependence of $E_G$ out to redshifts $z=2$ and higher, with photometric surveys having an advantage due to their large survey areas and high number densities. Finally, Advanced ACTPol CMB lensing cross-correlated with spectroscopic (photometric) surveys can differentiate between general relativity and modified gravity at the level of $3\sigma$ ($13\sigma$). Performing a $<1$% measurement of $E_G$ requires precision in $\beta$ on the order of 10%, which is currently achievable with a spectroscopic survey but will be difficult with only a photometric survey.
A. Pullen, S. Alam and S. Ho
Tue, 16 Dec 14
38/78
Comments: 10 pages, 7 figures, 4 tables, will submit to MNRAS
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