# Cosmología no estándar presente y futuro del Universo

- Pedro Felix González Díaz Director

Defence university: Universidad Autónoma de Madrid

Fecha de defensa: 19 July 2010

- Enrique Álvarez Vázquez Chair
- Antonio López Maroto Secretary
- Claudio Rubano Committee member
- Mar Bastero Gil Committee member
- Alfredo Tiemblo Ramos Committee member
- Pedro V. Oliveira Committee member
- Sergey D. Odintsov Committee member

Type: Thesis

## Abstract

The discovery of the cosmic acceleration indicated by the observational data [1; 2] has caused a break in the belief of what could be the matter content of the universe and what might be its possible future evolution. The interpretation of these data in the framework of General Relativity implies that the majority of the content in the universe should be a new stuff, which has been called dark energy. Dark energy is a fluid which possesses anti-gravitational properties, i.e. the equation of state parameter of the dark energy must be w < ¿1/3 (w = p/p). Therefore, this fluid violates at least the strong energy condition [3]. It is even possible that the equation of state parameter is less than ¿1. In that case, the new stuff is known as phantom energy [4] and the consideration of this fluid could lead the universe to a catastrophic end by the appearance of a future big rip singularity [5; 6]. The big rip is a possible doomsday of the universe where both its size and its energy density become infinite. Nevertheless, it is known that a phantom universe must not necessarilly finish in a doomsday if, for example, it has an equation of state of the form of a phantom generalized Chaplygin gas [7]. Owing to the strange properties of the phantom fluid, such as that its energy density increases with the scale factor, it seems quite natural that in a phantom universe some kind of cosmological objects even weirder than black holes may exist: traversable wormholes. These are short-cuts between two regions of the same universe or between two universes, which could be used to construct time-machines [8]. The reason for its strangeness is not only related to the bridge character they show, but also to that, in order to be traversable and stable, the wormholes must be surrounded by some kind of exotic matter which do not fulfil the null energy condition. The consideration of phantom models as the possible current description of the universe has caused a renaissance of traversable wormholes, since this fluid would also violate the null energy condition. Even more, it has been shown that an inhomogeneous version of phantom energy can be the exotic stuff which supports wormholes [9; 10; 11]. Dark energy, phantom or not, would therefore govern the future cosmic evolution, 5 6 ABSTRACT provided that this stuff is not decaying in another kind of energy. But this is not the only way in which dark energy could decide the future of the universe, since it can influence the dynamic evolution of some astronomical objects in such a way that they could even produce cosmological effects. On one hand, dark energy should be accreted onto black holes in a different way that ordinary matter does, since that new fluid covers the whole space. Therefore, the study of dark energy accretion onto black holes becomes an interesting field of study which could lead to surprising effects as the possible disappearance of black holes in a phantom environments [12]. On the other hand, in some cosmological models the accretion of phantom energy onto a wormhole could lead to an enormous growth of its mouth, which becomes so big that it is able to engulf the whole universe which would then become capable to travel through it in a big trip [13], avoiding the big rip singularity. In this dissertation we present the study of new phenomena related to the accelerated expansion of the universe under the assumption that dark energy is the responsible of such acceleration. Those new phenomena could be due: to the behavior of the universe itself, in some dark energy models, to the wormhole physical properties, or to the influence that black- and worm-holes could have at cosmological scales. Firstly, we deal with the acretion processes onto black- and worm-holes. The interesting results obtained about these processes in black holes [14] and wormholes [13] have been reconsidered when some approximations are suppressed. So, we extend the Babichev-Dokuchaev-Eroshenko model for the accretion of dark energy onto black holes, [14], to a non-static black hole case [15]. The possibility that a black hole with large mass will rapidly increase and eventually engulf the Universe at a finite time in the future is studied by using reasonable values for astronomical parameters. We conclude that, in this framework, such a phenomenon is forbidden for all black holes in 4-dimensional cosmological models [16]. We also include a first step in the consideration of the cosmological effects on that process, by using a generalized Schwarzschild-de Sitter metric [17]. In this case, the mentioned effects could magnify the black holes growth. Regarding the dark energy accretion onto wormholes, we also generalized the study of Ref. [13], dealing with a non-static metric. We reach the conclusion that the big trip process can actually occur, by using a method that now entails less approximation than in the black hole case [18]. Secondly, we consider some new phenomena which could be decisive in the future of the universe by studying some cosmological models and the implications of the accretion process in such models. In particular, we discuss on new cosmic solutions describing the early and late ABSTRACT 7 evolution of a universe that is filled with a kind of dark energy. Those models, [19], are obtained considering a dark energy fluid with a constant w in an scenario inspired in a Randall-Sundrum type 1 scenario [20]. The main distinctive property of the resulting space-times is that they make to appear twice the single singular events predicted by the corresponding dark energy models with w < ¿1 (w > ¿1), in a manner which can be made symmetric with respect to the origin of cosmic time. We also consider dark energy and phantom energy accretion onto black holes and wormholes in the context of these new cosmic solutions. It is seen that the space-times of these holes would then undergo swelling processes leading to big trip and big hole events taking place on distinct epochs along the evolution of the universe. In this way, the possibility is considered that the past and future be connected in a non-paradoxical manner in the universes described by means of the new symmetric solutions. Since it has been believed that models with phantom generalized Chaplygin gas (PGCG) do not contain singularities, we study next different PGCG models, reviewing what were previously studied [7]. We show that a PGCG model can present a future singularity in a finite future cosmic time [21; 22]. Unlike the big rip singularity, this singularity happens for a finite scale factor, but like the big rip singularity, it would also take place at a finite future cosmic time. In addition, we consider a Randall-Sundrum type 1 brane-world scenario, [20], where a dual of the generalised phantom Chaplygin gas (DPGCG) can be defined. We also show that the same kind of singularity at a finite scale factor can take place in this scenario [21; 22]. Whereas in the corresponding PGCG models the new singularity could be avoided by a big trip phenomenon, in the DPGCG that phenomenon would be absent [16]. We also present cosmic solutions corresponding to universes filled with dark and phantom energy, all having a negative cosmological constant [23]. All such solutions contain infinite singularities, successively and equally distributed along time, which can be either big bang/crunchs or big rips singularities. Classicaly, these solutions can be regarded as associated with multiverse scenarios, being those corresponding to phantom energy that may describe the current accelerating universe. The physical characteristics of that phantom classical multiverse scenario enable us to advance the following conjecture: whereas the physics of particles and fields is confined to live in the realm of the whole multiverse formed by finite-time single universes, that for our observable universe must be confined just in one of the infinite number of universes of the multiverse when such a universe is consistently referred to an infinite cosmic time. If this conjecture is adopted then some current fundamental problems that appear when one tries to make compatible particle physics and cosmology can be solved in this toy model [24]. 8 ABSTRACT Third, we consider the possible thermal emission made up of some sort of phantom radiation coming out from the wormhole and the formulation of the three main laws of wormholes thermodynamics [25; 26]. These results are obtained by analyzing the Hayward formalism of spherically symmetric solutions containing trapping horizons [27; 28], the mentioned phenomenon of phantom accretion onto wormholes and the development of phantom thermodynamics [29; 30]. Fourth, although we are considering that general relativity must be the theory which governs the gravitational interactions, there is another line of thinking which defends the necessity of modifying Einstein theory. In particular, we consider f(R)-gravity. Due to the mathematical equivalence of both frames, being related under conformal transformations, we study if such transformation would also imply a physical equivalence. With this purpose, we present a f(R)-cosmology with an exact analytic solution, coming from the request of the existence of a Noether symmetry [31], which is able to describe a dust-dominated decelerated phase before the current accelerated phase of the universe [32]. We compare this model with the corresponding model in the Einstein frame, related to each other by a conformal transformation, by obtaining observable physical quantities in both frames [33]. Since such observable quantities are different, both frames are not physically equivalents and one must decide what is the physical frame in order to discuss the results. Fifth, we try to understand the reasons which could be behind the distrust about the cosmological constant as responsible of the cosmic acceleration. With this aim in mind we discuss the origins of the cosmological constant, pointing out the different attempts for its revival, and briefly mentioning some possible theretical problems related with it. Nevertheless, if the reader want to insist in the consideration of this constant, then he/she must take into account that the universe will, in this case, develop into a de Sitter model. Far from implying a calmed future for such a model of the universe, in this scenario some phenomena could appear which are even more surprising than those discussed in this dissertation for the dark energy case; in particular, the nucleation of a Coleman-De Luccia bubble [34]. We present some preliminary results about the possible foliation of a de Sitter spacetime containing a de Sitter bubble in its interior, with a different value for the cosmological constant, by using constant mean curvature (CMC) hypersurfaces. In particular, we study in detail a foliation of this kind, showing that, in some cases, it can cover the existence of observers like us. We also include an argument which could help us to find other CMC foliations. Finally, we summarize the conclusions of this dissertation.