Implications of Dynamical Dark Energy in the expansion of the Universe and the Structure Formation

Abstract

En aquesta tesi s’estudien diferents models cosmològics, tots ells caracteritzats per considerar, de manera efectiva, una lleu evolució temporal de l’Energia Fosca, en contrast amb l’actual model estàndard de la cosmologia. El terme Energia Fosca s’utilitza per fer referència a una misteriosa forma d’energia que sembla impregnar tots els racons del Univers i que provoca que les galàxies s’allunyin les unes de les altres. El ritme predit d’expansió del Univers varia d’un model a un altre així com la quantitat d’estructura observada i la distribució d’aquesta. Degut al bon moment de la cosmologia observacional tenim a la nostre disposició una gran quantitat de dades que ens permeten posar a prova els diferents models existents. Un exemple d’aquests models, seria el Running Vacuum Model (RVM), que ha estat estudiat en detall en aquesta tesi i que considera una expressió per la densitat d’energia del buit motivada en el context de les Teories Quàntiques de Camp. Un altre exemple de models cosmològics serien els anomenats models de camp escalar que suposen que l’equació d’estat de l’Energia Fosca, en el moment present, és lleugerament diferent del valor predit pel model estàndard. No noées s’han considerat models acomodats dins del marc de la teoria de la Relativitat General, sinó que també s’han estudiat les prediccions teòriques del model presentat per Brans i Dicke al 1961 i que resulta ser el primer intent d’extensió de la teoria d’Einstein. El model de Brans i Dicke està caracteritzat pel fet que la interacció gravitatòria està no només mediada per un camp tensorial, sinó també per un camp escalar. Les prediccions teòriques dels diferents models estudiats, tant a nivell de background com a nivell de pertorbacions, han sigut contrastades amb les mes recents dades cosmològiques revelant que l'anteriorment esmentada evolució temporal de l’Energia Fosca ajuda a rebaixar, de manera considerable, algunes de les tensions que afecten al model estàndard. La comparació teoria-observacions s’ha dut a terme mitjançant una rigorosa metodologia que involucra diferents eines estadístiques. Per tant les conclusions obtingudes al llarg d’aquesta tesi es basen en un procés robust i en un estudi detallat dels diferents models cosmològics considerants.

The high quality observations performed during the last two decades, have allowed to demonstrate, with high confidence range, that the Universe is in expansion and to be more precise in accelerated expansion. In order to explain the accelerated evolution the name of dark energy was coined. It refers to a some mysterious form of diffuse energy presumably permeating all corners of the Universe as a whole. We may say that the canonical picture of our Universe defined in the framework of General Relativity, whose field equation were found by Einstein in 1917, is built upon the assumption that the observed acceleration is caused, in fact, by a rigid cosmological constant term denoted by Λ. Thanks to the aforementioned cosmological measurements, we have been able to pin down its value to an impressive level. Dark energy is not the only element, beyond the conventional baryons and photons, required by the observations since we also need large amounts of what is commonly call as dark matter. We call such an overall picture of the Universe the “concordance (or standard) cosmological model” or simply ΛCDM.

Therefore, we attribute the observed accelerated expansion of the Universe to the existence of a repulsive force, exerted by the Λ term, which works against the attractive gravitational force and tends to push the clusters of galaxies apart at a speed continuously increasing with the cosmic expansion.

Throughout this thesis a wide variety of models, beyond the standard model have been studied. The corresponding analyses have been carried out by studying in detail the theoretical predictions at the background and perturbation level, with the purpose of testing them with the large amount of cosmological data which we currently we have access to. The ultimate goal is to see if we can detect signals of new physics that help to alleviate some of the tensions that affect the ΛCDM. The concordance model, has remained robust and unbeaten for a long time since it is roughly consistent with a large body of cosmological data. Because of this fact, it is not reasonable to look for models with a very different behaviour than the ΛCDM, but to study models that exhibit small departures with respect to the standard model in key aspects.

We have studied the Running Vacuum Models (RVM) in depth. They are characterized by having a time-evolving vacuum energy density, whose functional expression is motivated in the context of Quantum Field Theory in curved space-time. It is fundamental that its expression contains a constant term, which mimics the standard behaviour in order to first generate the transition from a decelerated to an accelerated Universe and to ensure that the fit of the structure formation data is not ruined.

We have also studied the Peebles & Ratra model, which is a particularly successful scalar field model φCDM for which the potential takes the form V (φ) ∼ φ−α . The dimensionless parameter α encodes the extra degree of freedom that this model has with respect to the standard model. It is found to be small and positive, therefore V (φ) can mimic and approximate cosmological constant that is decreasing slowly with time. In the late Universe the contribution of the scalar field, φ, surfaces over the matter density, thus becoming the dominant component.

Not all the models studied are motivated within a theoretical framework, since we have also considered some interesting phenomenological approaches. Last but not least, at the end of the thesis the Brans & Dicke (BD) gravity model was studied in detail. The main feature of this model is that the Newtonian constant coupling GN is replaced by a dynamical scalar field G(t) = 1/ψ(t), coupled to the curvature. As a consequence the gravitational interaction is not only mediated by the metric field, as in the General Relativity case but also for the aforementioned scalar field ψ.

The obtained results clearly point out to an interesting conclusion, those models which consider an effective time-evolving dark energy are able to alleviate some of the tensions affecting the ΛCDM. Among the different tensions there are two that stand out, namely the σ8 -tension and the H0-tension.