Accelerated expansion from ghost-free bigravity: a statistical analysis
  with improved generality
  We study the background cosmology of the ghost-free, bimetric theory of
gravity. We perform an extensive statistical analysis of the model using both
frequentist and Bayesian frameworks and employ the constraints on the expansion
history of the Universe from the observations of supernovae, the cosmic
microwave background and the large scale structure to estimate the model's
parameters and test the goodness of the fits. We explore the parameter space of
the model with nested sampling to find the best-fit chi-square, obtain the
Bayesian evidence, and compute the marginalized posteriors and mean
likelihoods. We mainly focus on a class of sub-models with no explicit
cosmological constant (or vacuum energy) term to assess the ability of the
theory to dynamically cause a late-time accelerated expansion. The model
behaves as standard gravity without a cosmological constant at early times,
with an emergent extra contribution to the energy density that converges to a
cosmological constant in the far future. The model can in most cases yield very
good fits and is in perfect agreement with the data. This is because many
points in the parameter space of the model exist that give rise to
time-evolution equations that are effectively very similar to those of the
$\Lambda$CDM. This similarity makes the model compatible with observations as
in the $\Lambda$CDM case, at least at the background level. Even though our
results indicate a slightly better fit for the $\Lambda$CDM concordance model
in terms of the $p$-value and evidence, none of the models is statistically
preferred to the other. However, the parameters of the bigravity model are in
general degenerate. A similar but perturbative analysis of the model as well as
more data will be required to break the degeneracies and constrain the
parameters, in case the model will still be viable compared to the
$\Lambda$CDM.
