Tomographic Constraints on Gravity from Angular Redshift Fluctuations in the Late Universe

Abstract: Fluctuations in sky maps of the galaxy redshifts, dubbed as angular redshift fluctuations (ARF), contain precise information about the growth rate of structures and the nature of gravity in the Universe. Specifically, ARF constrain the combination of cosmological parameters $H/H_0\,f\sigma_8(z)$, while being an intrinsically tomographic probe and largely insensitive to many observational systematic errors, all this without requiring the assumption of any redshift-to-distance relation under a given fiducial cosmology. We present the first cosmological constraints derived from ARF by using BOSS LOWZ+CMASS DR12 galaxy samples, obtaining 7\%-accurate constraints on $H/H_0 f\sigma_8(z)$ at more than 20 redshifts over the range $z \in [0.26,0.72]$. Our best-fitting value is $10\%$ larger, but compatible at the $1.4\sigma$ level, than the $\Lambda$CDM expectation set by {\it Planck} observations of the Cosmic Microwave Background (CMB) radiation. Our tomographic measurements, combined with these CMB data, provides one of the strongest constraints on the gravity index $\gamma$, $\gamma=0.44^{+0.09}_{-0.07}$, which lies within $2\sigma$ from the prediction of General Relativity ($\gamma_{\rm GR}\simeq 0.55$).