Observational signatures of modified gravity on ultra-large scales

Extremely large surveys with future experiments like Euclid and the SKA will soon allow us to access perturbation modes close to the Hubble scale, with wavenumbers $k \sim \mathcal{H}$. If a modified gravity theory is responsible for cosmic acceleration, the Hubble scale is a natural regime for deviations from General Relativity (GR) to become manifest. The majority of studies to date have concentrated on the consequences of alternative gravity theories for the subhorizon, quasi-static regime, however. In this paper we investigate how modifications to the gravitational field equations affect perturbations around the Hubble scale. We choose functional forms to represent the generic scale-dependent behaviour of gravity theories that modify GR at long wavelengths, and study the resulting deviations of ultra large-scale relativistic observables from their GR behaviour. We find that these are small unless modifications to the field equations are drastic. The angular dependence and redshift evolution of the deviations is highly parameterisation- and survey-dependent, however, and so they are possibly a rich source of modified gravity phenomenology if they can be measured.