A Refined Einstein-Gauss-Bonnet Inflationary Theoretical Framework

Abstract

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 2 T = 1 in natural units, results to a constraint differential equation that relates the coupling function of the scalar field to the Gauss-Bonnet invariant ξ(φ) and the scalar potential V (φ). Adopting the slow-roll conditions for the scalar field and the Hubble rate, and in contrast to previous works, by further assuming that κ ξ ξ 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 ξ(φ) ∼ φ ν 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.

Red or blue tensor spectrum from GW170817-compatible Einstein-Gauss-Bonnet theory: A detailed analysis

“…Thus, both the potential and the second derivative of the scalar Gauss-Bonnet coupling function are negative, and so the tensor spectral index is positive. Indeed, as was shown in [102], for these values of the free parameters we have n T = [0.378, 0.379], hence it is positive and also one may verify that ξ(φ * )V (φ * ) > 0. Therefore, with our analysis one may know beforehand which Einstein-Gauss-Bonnet model may yield a blue-tilted tensor spectral index.…”

“…One string-originating theory that can produce a blue-tilted tensor spectral index is Einstein-Gauss-Bonnet theory, and for the mainstream of articles and reviews see refs. [91][92][93][94][95][96][97][98][99][100][101][102] and [5,[103][104][105][106] respectively.…”

“…Inflation with GW170817-compatible Einstein-Gauss-Bonnet theory and the tensor spectral index. Before we go to the core of our analysis, let us discuss the inflationary dynamics of GW170817-compatible Einstein-Gauss-Bonnet gravity which was developed in [101,102]. The Einstein-Gauss-Bonnet gravity action is the following:…”

“…Let us consider in brief some illustrative examples, the phenomenology of which is well studied in the literature and these provide a viable inflationary phenomenology [102]. Consider the following functional form of the scalar coupling function ξ(φ):…”

“…In this case, a viable phenomenology is guaranteed for the following values of the free parameters [102] μ = [22.091, 22.0914], β = −1.5, γ = 2, for N = 60 e-foldings. Thus, both the potential and the second derivative of the scalar Gauss-Bonnet coupling function are negative, and so the tensor spectral index is positive.…”