Eur. Phys. J. C (2016) 76: 40
https://doi.org/10.1140/epjc/s10052-016-3879-1

Regular Article - Theoretical Physics

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

¹ Department of Physics, National Taiwan University, Taipei, 10617, Taiwan
² LeCosPA, National Taiwan University, Taipei, 10617, Taiwan
³ Graduate Institute of Astrophysics, National Taiwan University, Taipei, 10617, Taiwan
⁴ Departamento de Física, Universidade da Beira Interior, 6200, Covilhã, Portugal
⁵ Centro de Matemática e Aplicações da Universidade da Beira Interior (CMA-UBI), 6200, Covilhã, Portugal
⁶ Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, 48080, Bilbao, Spain
⁷ IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain
⁸ SLAC National Accelerator Laboratory, Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA, 94305, USA

^* e-mail: b97202056@gmail.com

Received: 22 November 2015
Accepted: 27 December 2015
Published online: 22 January 2016

Abstract

In this paper, a modified Eddington-inspired-Born-Infeld (EiBI) theory with a pure trace term 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 . 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.