Reconstruction of Slow-roll $F(R)$ Gravity Inflation from the Observational Indices

TL;DR

This paper presents a bottom-up method to reconstruct $F(R)$ gravity models from specified observational indices, exemplified by a particular scalar-to-tensor ratio, ensuring compatibility with current data.

Contribution

It introduces a novel reconstruction technique fixing observational indices and deriving the corresponding $F(R)$ gravity, with analytical solutions for specific parameter choices.

Findings

Reconstructed $F(R)$ models align with observational data.

Analytical forms of $F(R)$ are obtained for specific parameter values.

The method links observational indices directly to gravity models.

Abstract

In this work, we introduce a bottom-up $F(R)$ gravity reconstruction technique, in which we fix the observational indices and we seek for the $F(R)$ gravity which may realize them. Particularly, as an exemplification of our method, we shall assume that the scalar-to-tensor ratio has a specific form, and from it we shall reconstruct the $F(R)$ gravity that may realize it, focusing on special values of the parameters in order to obtain analytical results. The observational indices we study are compatible with the latest observational data, and we discuss how the functional form of the observational indices may affect the viability of the model.