  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.
