Eur. Phys. J. C (2015) 75: 90
https://doi.org/10.1140/epjc/s10052-015-3257-4

Regular Article - Theoretical Physics

Eddington–Born–Infeld cosmology: a cosmographic approach, a tale of doomsdays and the fate of bound structures

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

^* e-mail: mbl@ubi.pt

Received: 8 July 2014
Accepted: 15 December 2014
Published online: 24 February 2015

Abstract

The Eddington-inspired-Born–Infeld scenario (EiBI) can prevent the big bang singularity for a matter content whose equation of state is constant and positive. In a recent paper [Bouhmadi-Lopez et al. (Eur. Phys. J. C 74:2802, 2014)] we showed that, on the contrary, it is impossible to smooth a big rip in the EiBI setup. In fact the situations are still different for other singularities. In this paper we show that a big freeze singularity in GR can in some cases be smoothed to a sudden or a type IV singularity under the EiBI scenario. Similarly, a sudden or a type IV singularity in GR can be replaced in some regions of the parameter space by a type IV singularity or a loitering behaviour, respectively, in the EiBI framework. Furthermore, we find that the auxiliary metric related to the physical connection usually has a smoother behaviour than that based on the physical metric. In addition, we show that bound structures close to a big rip or a little rip will be destroyed before the advent of the singularity and will remain bound close to a sudden, big freeze or type IV singularity. We then constrain the model following a cosmographic approach, which is well known to be model independent, for a given Friedmann–Lemaître–Robertson–Walker geometry. It turns out that among the various past or present singularities, the cosmographic analysis can pick up the physical region that determines the occurrence of a type IV singularity or a loitering effect in the past. Moreover, to determine which of the future singularities or doomsdays is more probable, observational constraints on the higher-order cosmographic parameters are required.