Canonical Scalar Field Inflation with String and $R^2$-Corrections

Understand

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 $\ddot\xi=H\dot\xi$, 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.