EiBI宇宙理論：宇宙論方法、末日預言與受縛系統的命運

Abstract

建立在Palatini方法上的Eddington-inspired-Born-Infeld 理論(EiBI)的一項重要特徵是它在真空中與愛因斯坦的廣義相對論相同，但是一旦有物質的存在，這個理論就會不同於廣義相對論。對於一個狀態方程是一個正值常數的物質而言，這個理論可以藉由一個反彈(bounce)或者迴盪效應(loitering effect)來消除大霹靂奇異點(Big Bang singularity)。我們發現在EiBI理論中，一個大撕裂(Big Rip)奇異點的消除是不可能的。但是當我們考慮其他奇異點的時候，就會得到不同的結果。確實，我們藉由EiBI理論試圖去避免/減緩其他對應到物理度規(physical metric)的暗能量奇異點。我們發現一個在廣義相對論中會出現的大凍結(Big Freeze)奇異點在EiBI理論中，會在某些情況下被減緩成一個突發(Sudden)或一個第四類(Type IV)奇異點。類似地，一個在廣義相對論中會出現的突發奇異點在EiBI理論中，會在某些參數範圍內被替代成一個第四類奇異點。並且，一個廣義相對論中的第四類奇異點也可以在某些情況下被替代成一個迴盪效應。再者，我們發現對於和物理聯絡(connection)相關的輔助度規(auxiliary metric)而言，它的奇異點效應會比物理度規還要平緩許多。另外，我們也展示了一個受縛系統的結構在接近大撕裂或小撕裂(Little Rip)之前會被破壞，但是在靠近突發、大凍結和第四類奇異點的時候則會維持受縛的狀態，這個結果和物理度規與輔助度規的選擇無關。接著，我們利用宇宙論方法--一個眾所皆知在給定的弗里德曼-勒梅特-羅伯遜-沃爾克度規(Friedmann-Lema^itre-Robertson-Walker metric)是模型獨立的方法--來制約這個模型。結果顯示，在眾多不同被這個理論預測的過去奇異點或者宇宙的起始之中，宇宙論分析偏向一個過去第四類奇異點或迴盪效應會發生的物理範圍。但是若要在這個理論預測的未來奇異點或宇宙末日之中決定確切的宇宙末日，我們需要對於更高階的宇宙論參數的觀測制約。除此之外我們還估計了這些過去和未來奇異點會發生的時間。 這篇論文是建立[1,2]這兩篇工作上。其中[1]已經被發表，而[2]也將在近期投稿發表。

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.