Tomographic constraints on gravity from angular redshift fluctuations in the late Universe

Fluctuations in sky maps of galaxy redshifts, dubbed angular redshift fluctuations (ARF), contain precise information about the growth rate of structures and the nature of gravity in the Universe. Specifically, ARFs 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 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 Baryon Oscillation Spectroscopic Survey (BOSS) LOWZ(Low redshift(Z))+CMASS(Constant MASS) DR12(Data Release 12) galaxy samples, obtaining 7 per cent accurate constraints on H/H₀fσ₈(z) at more than 20 redshifts over the range z ∈ [0.26, 0.72]. Our best-fitting value is $10{{\ \rm per\ cent}}$ larger, but compatible at the 1.4σ level, than the ΛCDM expectation set by Planck observations of cosmic microwave background (CMB) radiation. Our tomographic measurements, combined with these CMB data, provide one of the strongest constraints on the gravity index γ, $\gamma =0.44^{+0.09}_{-0.07}$ , which lies within 2σ of the prediction of General Relativity (γ_GR ≃ 0.55).