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

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-RobertsonWalker 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 a

Born–Infeld inspired modifications of gravity

“…These two behaviours can be visualised nicely by plotting the scale factor normalised by the scale a B as a function of time, which can be seen in figure 25. A more detailed analysis of these cosmological solutions was further investigated in [323,111,79,80,78].…”

“…The other polynomial whose cosmology has also been investigated is the first one, that was called Minimal model. The corresponding action is given by 80) where the constants have been chosen as to match GR without a cosmological constant in the low curvature regime. A possible cosmological constant term will be considered as part of the matter sector.…”

Kinetic theory of Jean instability in Eddington-inspired Born–Infeld gravity

“…One of the most interesting features is that EiBI is equivalent to GR in the vacuum while it introduces modifications in dense matter environments, where GR is experimentally not well probed. EiBI is able to describe, with only a single extra parameter (κ), astrophysical objects such as the Sun [19] and the internal structure of compact objects [20][21][22][23][24][25][26], and the cosmological expansion of the Universe [22,[27][28][29][30][31] (for comprehensive reviews see [7,12] and the references therein).…”

Quantum Cosmology of the Big Rip: Within GR and in a Modified Theory of Gravity

“…The EiBI theory has been shown to be able to remove the big bang singularity for a radiation-dominated universe through a loitering effect or a bounce in the past [26]. The ability of the theory to smooth other cosmological singularities in a phantom-dominated universe has also been studied in [35][36][37][38]. Unfortunately, it was found that even though the EiBI theory can lead to the avoidance of the big bang and the alleviation of some smoother singularities, the BR singularity is still unavoidable.…”