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

TL;DR

This paper investigates how the Eddington-inspired-Born-Infeld (EiBI) theory modifies various cosmological singularities, showing potential smoothing effects, and uses a model-independent cosmographic approach to constrain the model's predictions about the universe's fate.

Contribution

It demonstrates how EiBI gravity can alter the nature of cosmological singularities and applies cosmography to constrain the model's implications for the universe's evolution.

Findings

EiBI can smooth certain singularities like big freeze and type IV.

Auxiliary metric generally exhibits smoother behavior than the physical metric.

Cosmographic analysis helps identify the occurrence of specific singularities and loitering effects.

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 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 general relativity (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-Lema\^itre-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 higher order cosmographic parameters is required.