• inflation
• gravitational waves
• bimetric gravity
• stochastic background

In this thesis we focused on a bimetric theory of gravity that extends the theory of General Relativity by introducing an additional metric, to which is given its own dynamics. Moreover, associated with the additional metric, an entirely new matter sector is introduced, which could be seen as a copy of the usual Standard Model: it acts as a dark matter component, since it only interacts gravitationally with usual Standard Model particles. The theory is based on a exchange symmetry between both metrics and between both matter sectors: direct coupling terms between the metrics are absent and mass terms for the gravitons are not provided.
In absence of non-gravitational interactions, the dynamics of matter fields of different type is uniquely determined by the corresponding metric: the introduction of a second connection compatible with the additional metric is sufficient to describe the motion of the new particles in a background field. Nevertheless the introduction of two automorphism on the tensor bundle, named as pullovers, allows these newly introduced fields to have an effect on the geometry described by the standard metric: they become an additional, negatively weighed, source term to the Einstein equations.
In this context we studied the homogeneous and isotropic cosmological solutions described by two Friedmann Robertson Walker metrics assuming the presence of matter content of different type and we derived the corresponding Friedmann equations.
Then we focused on linear-order cosmological perturbation theory around the cosmological solutions in order to determine the evolution equations for tensor perturbations that describe the propagation of gravitational waves on cosmological distances, finding that gravitational waves sourced by the two metrics evolve independently with a friction term that takes into account only the Hubble parameter defined by the scale factor of the corresponding metric.
Considering such equations in an inflationary scenario leads to the phenomenon af amplification of vacuum fluctuations and consequently to the creation of a stochastic background of gravitational waves today. In this context we studied a modified model of inflation with respect to the standard single field slow-roll inflation, in which the inflationary dynamics is sourced by the presence of two scalar fields of different types.
We focused on the spectrum of tensor perturbations at first-order in the slow-roll expansion and we found that the deviation of the primordial gravitational waves power spectrum from scale invariance is parametrized by a tensor tilt, directy linked with the modified slow-roll parameters, that results consistently modified.