Probing gravity at large scales through CMB lensing

Understand

We describe a methodology to probe gravity with the cosmic microwave background (CMB) lensing convergence $\kappa$, specifically by measuring $E_G$, the ratio of the Laplacian of the gravitational scalar potential difference with the velocity divergence.

• Using CMB lensing instead of galaxy-galaxy lensing avoids intrinsic alignments while also lacking a hard limit on the lens redshift and 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 galaxy-CMB lensing and galaxy clustering angular power spectra, along with the RSD parameter $\beta$.