Canonical scalar field inflation with string and R2-corrections

Assuming that a scalar field controls the inflationary era, we examine the combined effects of string and f (R) gravity corrections on the inflationary dynamics of canonical scalar field inflation, imposing the constraint that the speed of the primordial gravitational waves is equal to that of light's. Particularly, we study the inflationary dynamics of an Einstein-Gauss-Bonnet gravity in the presence of alpha R-2 corrections, where alpha is a free coupling parameter. As it was the case in the pure Einstein-Gauss-Bonnet gravity, the realization that the gravitational waves propagate through spacetime with the velocity of light, imposes the constraint that the Gauss-Bonnet coupling function xi(phi) obeys the differential equation (sic) = H(xi)over dot where H is the Hubble rate. Subsequently, a relation for the time derivative of the scalar field is extracted which implies that the scalar functions of the model, which are the Gauss-Bonnet coupling and the scalar potential, are interconnected and simply designating one of them specifies the other immediately. In this framework, it is useful to freely designate xi(phi) and extract the corresponding scalar potential from the equations of motion but the opposite is still feasible. We demonstrate that the model can produce a viable inflationary phenomenology and for a wide range of the free parameters. Also, a mentionable issue is that when the coupling parameter a of the R-2 correction term is alpha < 10(-3) in Planck Units, the R-2 term is practically negligible and one obtains the same equations of motion as in the pure Einstein-Gauss-Bonnet theory, however the dynamics still change, since now the time derivative of partial derivative f/partial derivative R is nonzero. We study in detail the dynamics of inflation assuming that the slow-roll conditions hold true and also we briefly address the constant-roll case dynamics, and by using several illustrative examples, we compare the dynamics of the pure and R-2-corrected Einstein-Gauss-Bonnet gravity. Finally the ghosts issue is briefly addressed. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

This study explores the combined effects of string and f (R) gravity corrections on canonical scalar field inflation during the inflationary era controlled by a scalar field. By imposing the constraint that the primordial gravitational waves propagate at the speed of light, the dynamics of Einstein-Gauss-Bonnet gravity with alpha R-2 corrections are investigated. The research demonstrates the interconnectedness of Gauss-Bonnet coupling and scalar potential in the model, as well as the feasibility of extracting scalar potential from equations of motion when freely designating Gauss-Bonnet coupling xi(phi).