Exploring the inflation of F(R) gravity

Abstract

The early-time expansion of the spacetime, namely, inflation, is introduced to solve some cosmological problems. [Formula: see text] gravity is a simple extension of the general relativity to induce the inflationary expansion. The precise observation of the Cosmic Microwave Background gives us the information to inspect the model of the inflation. [Formula: see text] gravity can be transformed to the Einstein–Hilbert term with a scalar field that plays the role of the inflaton. The inflaton potential is described as an explicit function of the inflaton field with a noncanonical kinetic term. In this paper, we obtain general formulae to derive the inflationary parameters including the models with a noncanonical kinetic term. The inflationary parameters are described as functions of the inflaton potential and its derivatives. We evaluate a well-known model, [Formula: see text], to confirm the validity of our formulae. Then, we apply the procedure to a model, [Formula: see text], in which it is not possible to represent the potential as an explicit function of the inflaton field with a canonical kinetic term.