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 xi'/xi ''<< 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) similar to 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.

Automated summary

In this work, a refined Einstein-Gauss-Bonnet inflationary theoretical framework is provided, which is compatible with observational constraints on the gravitational wave speed. By introducing new assumptions and conditions, much simpler expressions for the slow-roll indices, tensor and scalar spectral indices, and tensor-to-scalar ratio are successfully derived. A particular model with a blue-tilted tensor spectral index is exemplified, showing compatibility with the latest Planck data and potential to describe the NANOGrav result according to recent literature.