Canonical scalar field inflation with string and [formula omitted]-corrections

Abstract

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 αR2 corrections, where α 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 ξ(ϕ) obeys the differential equation ξ̈=Hξ̇, 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 ξ(ϕ) 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 α of the R2 correction term is α<10−3 in Planck Units, the R2 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 ∂f∂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 R2-corrected Einstein–Gauss–Bonnet gravity. Finally the ghosts issue is briefly addressed.