Cascading dust inflation in Born-Infeld gravity
  In the framework of Born-Infeld inspired gravity theories, which deviates
from General Relativity (GR) in the high curvature regime, we discuss the
viability of Cosmic Inflation without scalar fields. For energy densities
higher than the new mass scale of the theory, a gravitating dust component is
shown to generically induce an accelerated expansion of the Universe. Within
such a simple scenario, inflation gracefully exits when the GR regime is
recovered, but the Universe would remain matter dominated. In order to
implement a reheating era after inflation, we then consider inflation to be
driven by a mixture of unstable dust species decaying into radiation. Because
the speed of sound gravitates within the Born-Infeld model under consideration,
our scenario ends up being predictive on various open questions of the
inflationary paradigm. The total number of e-folds of acceleration is given by
the lifetime of the unstable dust components and is related to the duration of
reheating. As a result, inflation does not last much longer than the number of
e-folds of deceleration allowing a small spatial curvature and large scale
deviations to isotropy to be observable today. Energy densities are
self-regulated as inflation can only start for a total energy density less than
a threshold value, again related to the species' lifetime. Above this
threshold, the Universe may bounce thereby avoiding a singularity. Another
distinctive feature is that the accelerated expansion is of the
superinflationary kind, namely the first Hubble flow function is negative. We
show however that the tensor modes are never excited and the tensor-to-scalar
ratio is always vanishing, independently of the energy scale of inflation.
