Inflationary f(R) cosmologies

Abstract

This paper discusses a simple procedure to reconstruct f(R)-gravity models from exact cosmological solutions of the Einstein field equations with a non-interacting classical scalar field-and-radiation background. From the type of inflationary scenario we are interested in, we show how the potential functions can be obtained. We then show how an f(R) gravitational Lagrangian density that mimics the same cosmological expansion as the scalar field-driven inflation of general relativity (GR) can be reconstructed. As a demonstration, we calculate the slow-roll parameters (the spectral index n s and the tensor-to-scalar ratio r) and compare these to the Planck data.