Inflation and the cosmological (not-so) constant in unimodular gravity
  We propose a mechanism for generating an inflationary phase in the early
universe without resorting to any type of scalar field(s). Instead, this
accelerated expansion is driven by a dynamical "cosmological constant" in the
framework of unimodular gravity. The time dependent cosmological constant can
be related to an energy diffusion term that arises naturally in unimodular
gravity due to its restrictive diffeomorphism invariance. We derive the generic
conditions required for any type of diffusion to generate a realistic
inflationary epoch. Furthermore, for a given parameterization of inflation (in
terms of the Hubble flow functions), we show how to construct the corresponding
diffusion term in such a way that a smooth transition occurs between inflation
and the subsequent radiation dominated era, hence reheating proceeds naturally.
The primordial spectrum is obtained during the inflationary phase by
considering inhomogeneous perturbations associated to standard hydrodynamical
matter (modeled as a single ultra-relativistic fluid). We demonstrate that the
resulting spectrum is equivalent to that obtained in traditional inflationary
models, and is also independent of the particular form of the diffusion term.
In addition, we analyze the feasibility of identifying the variable
cosmological constant, responsible for the inflationary expansion, with the
current observed value.
