# Born - Infeld-type modified gravity

## TL;DR

This paper introduces a modified Born-Infeld-type gravity model that unifies various gravity theories through a parameter, analyzes its solutions, stability, and cosmological implications, including inflation and critical points.

## Contribution

The paper proposes a new Born-Infeld-type gravity model with a parameter that interpolates between known models, analyzes its solutions, stability, and cosmological behavior.

## Key findings

- The model includes general relativity, Starobinsky, exponential, and other models as special cases.
- Bound on parameters from local tests constrains the model.
- The model can describe universe inflation and exhibits specific stability properties.

## Abstract

We propose and investigate the modified Born$-$Infeld-type gravity model with the function $F(R) = [1-(1-\beta R/\sigma)^\sigma]/\beta$. At different values of the dimensionless parameter $\sigma$ the action is converted into some models including general relativity ($\sigma=1$), the Starobinsky model ($\sigma=2$), the exponential model of gravity ($\sigma=\infty$), and a model proposed in [9], [10] ($\sigma=0.5$). A bound on the parameters, $\beta(1-\sigma)/\sigma\leq 2\times 10^{-6}$ cm$^2$, are due to local tests. The constant curvature solutions are obtained, and we found the potential, and the mass of the scalaron in the Einstein frame. The model describes the inflation of the universe. The de Sitter spacetime is unstable and a Minkovsky spacetime is stable. We investigate the cosmological parameters and some critical points of autonomous equations.