Gauge field back-reaction in Born Infeld cosmologies
  In this paper, we investigate the back-reaction of $U(1)$ gauge fields into a
class of inflationary settings. To be more precise, we employ a Bianchi-I
geometry (taken as an anisotropic perturbation of a flat FRW model) within two
types of Born-Infeld theories. Firstly we consider pure Born-Infeld
electromagnetism. For either a constant or a $b(\phi)$ coupling, inflationary
trajectories are modified but anisotropies increase; In particular, for the
former coupling we find that a quadratic inflaton potential, within a constant
ratio for the scalar and gauge energy densities, does not induce sufficient
inflation, while in the latter the back-reaction in the cosmology determines
(from the tensor-scalar ratio) a narrow range where inflation can occur. A
Dirac-Born-Infeld framework is afterwards analysed in both non-relativistic and
relativistic regimes. In the former, for different cases of the coupling
(richer with respect to mere BI setups) between scalar and gauge sectors, we
find that inflationary trajectories are modified, with anisotropy increasing or
decreasing. In particular, a tachyonic solution is studied, allowing for a non
standard ratio between scalar and gauge matter densities, enhancing sufficient
inflation, but with the anisotropy increasing. For the relativistic limit,
inflationary trajectories are also modified and anisotropies increase faster
than in the non-relativistic limit. Finally we discuss how magnetic seed fields
could evolve in these settings.
