Exploring the hidden essence of the Cosmos

The present thesis is aimed to disclose three genuine phantom Dark Energy (DE) models where each of them induce a particular cosmic doomsday. We have named these models as model A, model B and model C, while the corresponding induced cosmic events are known as Big Rip (BR), Little Rip (LR) and Little Sibling of the Big Rip (LS), respectively. We regard a BR as a true singularity since it takes place at a finite cosmic time, while we have coined LR and LS as abrupt events, since they occur at infinite cosmic time. Nevertheless, it is well known that in such abrupt events sooner or later all the bound structures would unavoidably torn away, and therefore, the Universe would face a total destruction at a finite cosmic time. On the one side, we have addressed the background phenomenology and the first order cosmological perturbations for the phantom DE models above mentioned. In addition, we have made use of the widely known ΛCDM model as a guideline to measure deviations among the models. Given that a DE content is present, we avoid the associated instabilities at the perturbative level by applying the method of DE pressure decomposition in its adiabatic and non‐adiabatic contributions. We compute, by means of numerical methods, the evolution of the perturbed quantities for a Universe filled with radiation, matter and DE. Such computations are carried from well inside the radiation dominated era to the far future. Then, we predict the current matter power spectrum and fσ8 growth rate for each model. The latter mentioned observable quantity is compared with the current observational data in order to find footprints that could allow us to distinguish between the mentioned models. For the sake of completeness, we have fitted observationally these phantom DE models together with ΛCDM in order to constrain the parameters characterising the models. On the one hand, we have found that despite that ΛCDM still gives the best fit, it is closely followed by the models studied in the present thesis. On the other hand, we have found that these genuine phantom models induce a sign switch of the gravitational potential at very large scale factors. This fact could be understood as gravity becoming effectively repulsive in the far future. Finally, we have studied the effects of DE speed of sound on the perturbations. On the other side, it is expected that quantum effects will become important when the Universe approaches a future cosmic singularity, which is the case of those events addressed in the present thesis. Unfortunately, we have not yet a consistent theory of quantum gravity to deal with the most dramatic effects that would take place at the end of the Universe. It is expected that such a fundamental quantum theory of gravity will naturally avoid those singularities present in the classical theory of General Relativity (GR). We have rather addressed the issue of cosmological singularity avoidance within the context of a quantum approach. The quantisation is carried via Wheeler‐DeWitt (WDW) equation and imposing the DeWitt (DW) boundary condition, i.e. the wave function vanishes close to the singularity. We have analysed each model by considering different factor orderings and solving the WDW equation for a DE content given by (i), a perfect fluid, and (ii), a scalar field. In addition, we have addressed these phantom models in the context of the Eddington‐inspired‐Born‐Infeld (EiBI) modified theory of gravity and applied the same quantisation methods above mentioned to analyse the avoidance of singularities from a quantum point of view. Therefore, this thesis is divided in two main parts, a classical part, where we present the back-ground and perturbations of three genuine phantom models, and a second part, where we address the avoidance of singularities induced by such models from a quantum point of view. Given that UBI allows to present the thesis as an introduction, a set of chapters based on the published works during the PhD and the conclusions, we have followed mainly this format.A tese presente tem por objetivo estudar e comparar três modelos com energia escura fantasma, onde cada um induz um cenário cosmológico extremo de extinção do Universo. Escolhemos identificar esses três modelos como: modelo A, modelo B e modelo C, enquanto as extinções cósmicas correspondentes são conhecidas como Big Rip (BR), Litlle Rip (LR) e Little Sibling of the Big Rip (LS), respetivamente. Encaramos o BR como uma verdadeira singularidade, uma vez que esta acontece ao fim de um intervalo de tempo cósmico finito, enquanto identificamos o LR e LS como acontecimentos abruptos, porque estes ocorrem ao fim de intervalo de tempo cósmico que tende para infinito. Contudo, é reconhecido que em tais acontecimentos abruptos, mais cedo ou mais tarde, todas as estruturas ligadas serão inevitavelmente destruídas e, portanto, o Universo iria confrontar‐se com uma destruição total num intervalo de tempo cósmico finito. Numa primeira abordagem ao assunto da tese, considerámos a fenomenologia das soluções de fundo e as perturbações de primeira ordem cosmológicas para os modelos de energia escura fantasma acima mencionados. Adicionalmente, usámos o largamente conhecido modelo ΛCDM como padrão em relação ao qual se estimam os desvios dos modelos considerados. Uma vez que o conteúdo de energia escura está presente, evitamos o surgimento das instabilidades associadas através da decomposição da pressão da energia escura nas contribuições adiabáticas e não adiabáticas. Calculamos, através de métodos numéricos, a evolução das quantidades perturbadas para um Universo contendo radiação, matéria e energia escura. Estes cálculos são feitos assumindo um ponto de partida bem no interior da era dominada pela radiação até ao futuro longínquo. Subsequentemente, prevemos o espetro de potência atual e a taxa de crescimento fσ8 para cada modelo. Tais quantidades observáveis são, então, comparadas com os dados observacionais correntes de modo a encontrar indícios que nos permitiriam distinguir os diversos modelos na época atual. Por forma a completar o estudo, impusemos constrangimentos observacionais aos modelos de energia escura fantasma com o ΛCDM para obter um conjunto consistente de parâmetros. Por um lado, descobrimos que embora o ΛCDM se ajuste melhor às observações, os modelos aqui considerados seguem de muito perto esse bom ajuste do modelo padrão. Por outro lado, descobrimos que estes modelo genuínos de energia escura fantasma induzem uma inversão de sinal do potencial gravítico para fatores de escala muito grandes. Este facto pode ser interpretado como a força da gravidade se tornar efetivamente repulsiva num futuro distante. Finalmente, estudámos os efeitos de variar a velocidade efetiva do som da energia escura nas perturbações. Numa segunda abordagem, partimos do princípio que é expectável que os efeitos quânticos se tornem importantes quando o Universo se aproxima de uma singularidade cósmica futura, o que se afigura o destino certo nos modelos considerados anteriormente. Infelizmente, não dispomos ainda de uma teoria quântica da gravidade consistente para completar a nossa visão sobre os acontecimentos mais dramáticos no fim da vida do Universo. É esperado que com a ajuda de uma teoria tão fundamental, como a teoria quântica do campo gravítico, os cenários singulares previstos na Relatividade Geral sejam naturalmente evitados. Assim, abordámos o problema da remoção das singularidades cosmológicas adotando uma abordagem quântica. A quantização é implementada através da equação de Wheeler‐DeWitt e a imposição da condição fronteira de DeWitt, isto é, considerando que a função de onda se anula perto da singularidade. Analisámos cada modelo considerando várias ordens dos fatores na construção dos observáveis na equação de Wheeler‐DeWitt, resolvendo‐a para vários conteúdos da energia escura dados por (i), um fluido perfeito, e (ii), um campo escalar. Adicionalmente, considerámos estes modelos no contexto da teoria de gravidade modificada Eddington‐inspired‐Born‐Infeld e aplicámos a abordagem quântica, acima descrita, para remover as singularidades clássicas. Deste modo, esta tese é dividida em duas partes principais, uma clássica, onde descrevemos as soluções de fundo e as perturbações desse fundo para os três modelos genuínos de energia escura fantasma e, uma segunda parte onde estudamos a remoção quântica das singularidades resultantes destes modelos. Dado que a UBI permite que se apresente uma tese que inclua uma introdução, um conjunto de capítulos baseados em trabalhos publicados durante o Doutoramento e as conclusões, nós seguimos principalmente esse formato

What if gravity becomes really repulsive in the future?

The current acceleration of the Universe is one of the most puzzling issues in theoretical physics nowadays. We are far from giving an answer on this letter to its true nature. Yet, with the observations we have at hand, we analyse the different patterns that the gravitational potential can show in the future. Surprisingly, gravity not only can get weaker in the near future, it can even become repulsive; or equivalently, the gravitational potential may become negative. We show this remark by using one of the simplest phenomenological model we can imagine for dark energy. We have as well reviewed the statefinder approach of these models. For completeness, we have also showed the behaviour of the density contrast of dark matter and dark energy for these simple (yet illustrative models). Our results are displayed at present and how they evolve in the future.Comment: 7 pages, 3 figures. Further explanations provided. Version accepted in EPJ

Doomsdays in a modified theory of gravity: A classical and a quantum approach

By far cosmology is one of the most exciting subject to study, even more so with the current bulk of observations we have at hand. These observations might indicate different kinds of doomsdays, if dark energy follows certain patterns. Two of these doomsdays are the Little Rip (LR) and Little Sibling of the Big Rip (LSBR). In this work, aside from proving the unavoidability of the LR and LSBR in the Eddington-inspired-Born-Infeld (EiBI) scenario, we carry out a quantum analysis of the EiBI theory with a matter field, which, from a classical point of view would inevitably lead to a universe that ends with either LR or LSBR. Based on a modified Wheeler-DeWitt equation, we demonstrate that such fatal endings seems to be avoidable.Comment: 6 pages. A more careful and detailed analysis of the classical and quantum Hamiltonian included. Physical results unchanged. Version accepted in PL

Cosmological Perturbations in Phantom Dark Energy Models

The CDM paradigm, characterised by a constant equation of state w = -1 for dark energy, is the model that better fits observations. However, the same observations strongly support the possibility of a dark energy content where the corresponding equation of state is close to but slightly smaller than -1. In this regard, we focus on three different models where the dark energy content is described by a perfect fluid with an equation of state which can evolve or not. The three proposals show very similar behaviour at present, while the asymptotic evolution of each model drives the Universe to different abrupt events known as (i) Big Rip; (ii) Little Rip (LR); and (iii) Little Sibling of the Big Rip. With the aim of comparing these models and finding possible imprints in their predicted matter distribution, we compute the matter power spectrum and the growth rate fs. We conclude that the model which induces a LR seems to be favoured by observations.The work of I. A. was supported by a Santander-Totta fellowship "Bolsas de Investigacao Faculdade de Ciencias (UBI) - Santander Totta". The work of M.B.-L. is supported by the Portuguese Agency "Fundacao para a Ciencia e Tecnologia" through an Investigador FCT Research contract, with reference IF/01442/2013/CP1196/CT0001. She also wishes to acknowledge the partial support from the Basque government Grant No. IT592-13 (Spain) and FONDOS FEDER under grant FIS2014-57956-P (Spanish government). This research work is partially supported by the grant UID/MAT/00212/2013. J.M. is thankful to UPV/EHU for a PhD fellowship and acknowledges the support from the Basque government Grant No. IT592-13 (Spain) and FONDOS FEDER, under grant FIS2014-57956-P (Spanish Government). The authors acknowledge the COST Action CA15117 (CANTATA)

A varying Dark Energy effective speed of sound parameter in the phantom Universe

We analyse the phenomenological effects of a varying Dark Energy (DE) effective speed of sound parameter, $c^{2}_{\textrm{sd}}$, on the cosmological perturbations of three phantom DE models. Each of these models induce a particular abrupt future event known as Big Rip (BR), Little Rip (LR), and Little Sibling of the Big Rip (LSBR). In this class of abrupt events, all the bound structures in the Universe would be ripped apart at a finite cosmic time. We compute the evolution of the perturbations, $f\sigma_{8}$ growth rate and forecast the current matter power spectrum. We vary the $c^{2}_{\textrm{sd}}$ parameter in the interval $[0,1]$ and compute the relative deviation with respect $c^{2}_{\textrm{sd}}=1$. In addition, we analyse the effect of gravitational potential sign flip that occurs at very large scale factors as compared with the current one.Comment: 15 pages, 6 figures. Improved version with an extended physical discussion. Version published in EPJ

Quantum cosmology of Eddington-Born-Infeld gravity fed by a scalar field: the big rip case

We study the quantum avoidance of the big rip singularity in the Eddington-inspired-Born-Infeld (EiBI) phantom model. Instead of considering a simple phantom dark energy component, which is described by a perfect fluid, we consider a more fundamental degree of freedom corresponding to a phantom scalar field with its corresponding potential, which would lead the classical universe to a big rip singularity. We apply a quantum geometrodynamical approach by performing an appropriate Hamiltonian study including an analysis of the constraints of the system. We then derive the Wheeler-DeWitt (WDW) equation and see whether the solutions to the WDW equation satisfy the DeWitt boundary condition. We find that by using a suitable Born-Oppenheimer (BO) approximation, whose validity is proven, the DeWitt condition is satisfied. Therefore, the big rip singularity is expected to be avoided in the quantum realm.Comment: 12 page