Modified Eddington-inspired-Born-Infeld Gravity with a Trace Term

TL;DR

This paper introduces a modified EiBI gravity model with a trace term, leading to smooth bouncing cosmologies, potential inflationary phases without exotic matter, and a new type of finite-time singularity.

Contribution

It presents the first analysis of a trace term in EiBI gravity within the Palatini formalism, revealing novel cosmological solutions and singularity behaviors.

Findings

Enables smooth bouncing solutions absent in standard EiBI.

Allows natural de Sitter inflation in radiation-dominated universe.

Identifies a new 'quasi-sudden' finite-time singularity.

Abstract

In this paper, a modified Eddington-inspired-Born-Infeld (EiBI) theory with a pure trace term $g_{\mu\nu}R$ being added to the determinantal action is analysed from a cosmological point of view. It corresponds to the most general action constructed from a rank two tensor that contains up to first order terms in curvature. This term can equally be seen as a conformal factor multiplying the metric $g_{\mu\nu}$. This very interesting type of amendment has not been considered within the Palatini formalism despite the large amount of works on the Born-Infeld-inspired theory of gravity. This model can provide smooth bouncing solutions which were not allowed in the EiBI model for the same EiBI coupling. Most interestingly, for a radiation filled universe there are some regions of the parameter space that can naturally lead to a de Sitter inflationary stage without the need of any exotic matter field. Finally, in this model we discover a new type of cosmic "quasi-sudden" singularity, where the cosmic time derivative of the Hubble rate becomes very large but finite at a finite cosmic time.