We investigate the cosmology of SO(3)-invariant massive gravity with 5 degrees of freedom. In contrast with previous studies, we allow for a non-trivial fiducial metric, which can be justified by invoking, for example, a dilaton-like global symmetry.
We write the homogeneous and isotropic equations of motion in this more general setup and identify, in particular, de Sitter solutions. We then study the linear perturbations around the homogeneous cosmological solutions, by deriving the quadratic Lagrangian governing the dynamics of scalar, vector and tensor modes. We thus obtain the conditions for the perturbations to be well-behaved. We show that it is possible to find de Sitter solutions whose perturbations are weakly coupled and stable, i.e. without ghost-like or gradient instabilities.
Gauge-flation is a recently proposed model in which inflation is driven solely by a non-Abelian gauge field thanks to a specific higher order derivative operator. The nature of the operator is such that it does not introduce ghosts. We compute the co
smological scalar and tensor perturbations for this model, improving over an existing computation. We then confront these results with the Planck data. The model is characterized by the quantity gamma = (g^2 Q^2)/H^2 (where g is the gauge coupling constant, Q the vector vev, and H the Hubble rate). For gamma < 2, the scalar perturbations show a strong tachyonic instability. In the stable region, the scalar power spectrum n_s is too low at small gamma, while the tensor-to-scalar ratio r is too high at large gamma. No value of gamma leads to acceptable values for n_s and r, and so the model is ruled out by the CMB data. The same behavior with gamma was obtained in Chromo-natural inflation, a model in which inflation is driven by a pseudo-scalar coupled to a non-Abelian gauge field. When the pseudo-scalar can be integrated out, one recovers the model of Gauge-flation plus corrections. It was shown that this identification is very accurate at the background level, but differences emerged in the literature concerning the perturbations of the two models. On the contrary, our results show that the analogy between the two models continues to be accurate also at the perturbative level.
