Fourth-order gravity as the inflationary model revisited

TL;DR

This paper revisits the Starobinsky inflation model based on fourth-order gravity, deriving the scalar potential and computing inflation observables, confirming the equivalence between f(R) gravity and scalar-tensor theories, and comparing results with WMAP5 data.

Contribution

It provides a detailed derivation of the inflaton potential from fourth-order gravity and computes precise inflation observables including next-to-leading-order corrections.

Findings

Derived the scalar potential from f(R) gravity using Legendre-Weyl transform.

Calculated inflation observables with next-to-leading-order corrections.

Confirmed the equivalence between f(R) gravity and scalar-tensor models.

Abstract

We revisit the old (fourth-order or quadratically generated) gravity model of Starobinsky in four space-time dimensions, and derive the (inflaton) scalar potential in the equivalent scalar-tensor gravity model via a Legendre-Weyl transform. The inflaton scalar potential is used to compute the (CMB) observables of inflation associated with curvature perturbations (namely, the scalar and tensor spectral indices, and the tensor-to-scalar ratio), including the new next-to-leading-order terms with respect to the inverse number of e-foldings. The results are compared to the recent (WMAP5) experimental bounds. We confirm both mathematical and physical equivalence between f(R) gravity theories and the corresponding scalar-tensor gravity theories.