Viable Inflationary Models in a Ghost-free Gauss-Bonnet Theory of
  Gravity
  In this work we investigate the inflationary phenomenological implications of
a recently developed ghost-free Gauss-Bonnet theory of gravity. The resulting
theory can be viewed as a scalar Einstein-Gauss-Bonnet theory of gravity, so by
employing the formalism for cosmological perturbations for the latter theory,
we calculate the slow-roll indices and the observational indices, and we
compare these with the latest observational data. Due to the presence of a
freely chosen function in the model, in principle any cosmological evolution
can be realized, so we specify the Hubble rate and the freely chosen function
and we examine the phenomenology of the model. Specifically we focus on de
Sitter, quasi-de Sitter and a cosmological evolution in which the Hubble rate
evolves exponentially, with the last two being more realistic choices for
describing inflation. As we demonstrate, the ghost-free model can produce
inflationary phenomenology compatible with the observational data. We also
briefly address the stability of first order scalar and tensor cosmological
perturbations, for the exponential Hubble rate, and as we demonstrate,
stability is achieved for the same range of values of the free parameters that
guarantee the phenomenological viability of the models.
