EiBI宇宙理論：宇宙論方法、末日預言與受縛系統的命運

Abstract

The Eddington-inspired-Born-Infeld scenario (EiBI) extit{`{a} la} Palatini approach is characterised by being equivalent to Einstein theory in vacuum but differing from it in the presence of matter. This theory prevents the Big Bang singularity either through a bounce or a loitering effect for a matter content whose equation of state is constant and positive. We show the impossibility of smoothing a big rip on the EiBI setup. The story is quite different for other singularities. Indeed, we invoke the EiBI scenario as a mean to avoid/smooth other dark energy related singularities with respect to the physical metric. We show that a big freeze singularity in general relativity (GR) can be smoothed in the EiBI scenario in some cases, where the singularity is substituted by a sudden or a type IV singularity. Similarly, a sudden singularity in GR can be replaced in some regions of the parameter space by a type IV singularity in the EiBI framework. And a type IV singularity can be replaced in some cases by a loitering behaviour. Furthermore, we also find that the auxiliary metric related to the physical connection usually has a smoother behaviour than the physical metric. In addition, we show that bound structures close to a big rip or 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. This result is independent of the choice of the physical or auxiliary metric. Subsequently, we constrain the model following a cosmographic approach which is well known to be theoretically model independent for a given Friedmann-Lema^itre-Robertson-Walker geometry. It turns out that among the various past singularities or beginning predicted by the theory, the cosmographic analyses pick up the physical region which determines the occurrence of a type IV singularity or a loitering effect in the past. While among the various future singularities or doomsday predicted, the use of observational constraints on higher order cosmographic parameters is necessary to predict which doomsday is more probable. We estimate as well when those singularities would happen in the future or in the past. The thesis is based on the works [1,2]. [1] is already published and [2] is about to be submitted for publication.