Searching for modified gravity: scale and redshift dependent constraints from galaxy peculiar velocities

We present measurements of both scale- and time-dependent deviations from the standard gravitational field equations. These late-time modifications are introduced separately for relativistic and non-relativistic particles, by way of the parameters Gmatter(k, z) and Glight(k, z) using two bins in both scale and time, with transition wavenumber 0.01 Mpc−1 and redshift 1. We emphasize the use of two dynamical probes to constrain this set of parameters, galaxy power-spectrum multipoles and the direct peculiar velocity power spectrum, which probe fluctuations on different scales. The multipole measurements are derived from the WiggleZ and Baryon Oscillation Spectroscopic Survey (BOSS) CMASS galaxy redshift surveys and the velocity power spectrum is measured from the velocity sub-sample of the 6-degree Field Galaxy Survey. We combine these measurements with additional cosmological probes. Using a Markov Chain Monte Carlo likelihood analysis, we find the inferred best-fitting parameter values of Gmatter(k, z) and Glight(k, z) to be consistent with the standard model at the 95 per cent confidence level. We expand this analysis by performing Bayesian model selection between our phenomenological model and general relativity. Using the evidence ratio we find ‘no support’ for including modifications to general relativity. Furthermore, accounting for the Alcock–Paczynski effect, we perform joint fits for the expansion history and growth index gamma; we measure γ = 0.665 ± 0.067 (68 per cent CL) for a fixed expansion history, and γ=0.73+0.08−0.10 (68 per cent CL) when the expansion history is allowed to deviate from Λ cold dark matter. For the latter case, we observe a 2σ tension with the standard model where γ = 0.554.