# Born-Infeld gravity with a Brans-Dicke scalar

## TL;DR

This paper introduces a scalar-tensor extension of Born-Infeld gravity inspired by Brans-Dicke theory, allowing the BI parameter to vary dynamically, which leads to new cosmological behaviors including late-time acceleration without dark energy.

## Contribution

It proposes a novel scalar-tensor Born-Infeld gravity model with a spacetime-dependent BI parameter, expanding the theory's applicability and addressing issues of parameter sign and value.

## Key findings

- Deviations from general relativity in weak-field cosmology.
- Late-time acceleration without dark energy.
- Flexible BI parameter eliminates fixed sign constraints.

## Abstract

Recently proposed Born-Infeld (BI) theories of gravity assume a constant BI parameter ($\kappa$). However, no clear consensus exists on the sign and value of $\kappa$. Recalling the Brans-Dicke (BD) approach, where a scalar field was used to generate the gravitational constant $G$, we suggest an extension of Born-Infeld gravity with a similar Brans-Dicke flavor. Thus, a new action, with $\kappa$ elevated to a spacetime dependent real scalar field, is proposed. We illustrate this new theory in a cosmological setting with pressureless dust and radiation as matter. Assuming a functional form of $\kappa(t)$, we numerically obtain the scale factor evolution and other details of the background cosmology. It is known that BI gravity differs from general relativity (GR) in the strong-field regime but reduces to GR for intermediate and weak fields. Our studies in cosmology demonstrate how, with this new, scalar-tensor BI gravity, deviations from GR as well as usual BI gravity, may arise in the weak-field regime too. For example, we note a late-time acceleration without any dark energy contribution. Apart from such qualitative differences, we note that fixing the sign and value of $\kappa$ is no longer a necessity in this theory, though the origin of the BD scalar does remain an open question.