A Refined Einstein-Gauss-Bonnet Inflationary Theoretical Framework
  We provide a refined and much more simplified Einstein-Gauss-Bonnet
inflationary theoretical framework, which is compatible with the GW170817
observational constraints on the gravitational wave speed. As in previous
works, the constraint that the gravitational wave speed is $c_T^2=1$ in natural
units, results to a constraint differential equation that relates the coupling
function of the scalar field to the Gauss-Bonnet invariant $\xi(\phi)$ and the
scalar potential $V(\phi)$. Adopting the slow-roll conditions for the scalar
field and the Hubble rate, and in contrast to previous works, by further
assuming that $\kappa \frac{\xi '}{\xi''}\ll 1$, which is motivated by
slow-roll arguments, we succeed in providing much more simpler expressions for
the slow-roll indices and for the tensor and scalar spectral indices and for
the tensor-to-scalar ratio. We exemplify our refined theoretical framework by
using an illustrative example with a simple power-law scalar coupling function
$\xi(\phi)\sim \phi^{\nu}$ and as we demonstrate the resulting inflationary
phenomenology is compatible with the latest Planck data. Moreover, this
particular model produces a blue-tilted tensor spectral index, so we discuss in
brief the perspective of describing the NANOGrav result with this model as is
indicated in the recent literature.
