Red or Blue Tensor Spectrum from GW170817-compatible Einstein-Gauss-Bonnet Theory: A Detailed Analysis

Abstract

In this work we shall prove that the tensor spectral index of the primordial tensor perturbations for GW170817-compatible Einstein-Gauss-Bonnet theories, takes the approximate simplified form nT≃2(-1+ 1/λ(φ))ϵ1 at leading order, with λ(φ) being a function of the scalar field which depends on the scalar field potential and the second derivative of the scalar-Gauss-Bonnet coupling ξH(φ). With our analysis we aim to provide a definitive criterion for selecting Einstein-Gauss-Bonnet models that can provide a blue-tilted inflationary phenomenology, by simply looking at the scalar potential and the scalar-Gauss-Bonnet coupling. We shall prove this using two distinct approaches and as we show the tilt of the tensor spectral index is determined by the values of the potential V(φ) and of scalar-Gauss-Bonnet coupling at first horizon crossing. Specifically the blue-tilted tensor spectral index can occur when ξH(φ˙)V (φ˙) > 0 at first horizon crossing.