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We address the quantisation of a model that induces the Little Sibling of the Big Rip (LSBR) abrupt event, where the dark energy content is described by means of a phantom-like fluid or a phantom scalar field. The quantisation is done in the framework of the Wheeler-DeWitt (WDW) equation and imposing the DeWitt boundary condition; i.e., the wave function vanishes close to the abrupt event. We analyse the WDW equation within two descriptions: First, when the dark energy content is described with a perfect fluid. This leaves the problem with the scale factor as the single degree of freedom. Second, when the dark energy content is described with a phantom scalar field in such a way that an additional degree of freedom is incorporated. Here, we have applied the Born-Oppenheimer (BO) approximation in order to simplify the WDW equation. In all cases, the obtained wave function vanishes when the LSBR takes place, thus fulfilling the DeWitt boundary condition. [ABSTRACT FROM AUTHOR]

Assuming both that our Universe is evolving into a de Sitter space and a vanishing cosmological constant, leaves only the option that the observed acceleration is provided by a “kinetic” energy of a scalar field. From an effective field theory point of view, the absence of Ostrogradsky instabilities restricts the choice to shift-symmetric Horndeski theories. Within these theories, we find the conditions for the existence of a de Sitter critical point in a universe filled by matter, radiation and a Horndeski scalar. Moreover, we show that this point is a universal attractor and we provide the tracking trajectory. Therefore, if a de Sitter fixed point exists within these models, our Universe will eventually evolve into a de Sitter space. As an example, we have discussed the case of the combined Galileon–Slotheon system, in which the Galileon is kinetically non-minimal coupled to the Einstein tensor. Interestingly, we have also found that the tracker trajectory of this system does not follow previous literature assumptions. [ABSTRACT FROM AUTHOR]

We explore the dynamics and evolution of the Universe at early and late times, focusing on both dark energy and extended gravity models and their astrophysical and cosmological consequences. Modified theories of gravity not only provide an alternative explanation for the recent expansion history of the universe, but they also offer a paradigm fundamentally distinct from the simplest dark energy models of cosmic acceleration. In this review, we perform a detailed theoretical and phenomenological analysis of different modified gravity models and investigate their consistency. We also consider the cosmological implications of well motivated physical models of the early universe with a particular emphasis on inflation and topological defects. Astrophysical and cosmological tests over a wide range of scales, from the solar system to the observable horizon, severely restrict the allowed models of the Universe. Here, we review several observational probes--including gravitational lensing, galaxy clusters, cosmic microwave background temperature and polarization, supernova and baryon acoustic oscillations measurements--and their relevance in constraining our cosmological description of the Universe. [ABSTRACT FROM AUTHOR]

In this essay, we propose that the theory of gravity's vacuum is described by a de Sitter geometry. Under this assumption, we consider an adjustment mechanism able to screen any value of the vacuum energy of the matter fields. We discuss the most general scalar-tensor cosmological models with second-order equations of motion that have a fixed de Sitter critical point for any kind of material content. These models give rise to interesting cosmological evolutions that we shall discuss. [ABSTRACT FROM AUTHOR]

In this paper, we present a new cosmological event, which we named the little sibling of the big rip. This event is much smoother than the big rip singularity. When the little sibling of the big rip is reached, the Hubble rate and the scale factor blow up, but the cosmic derivative of the Hubble rate does not. This abrupt event takes place at an infinite cosmic time where the scalar curvature explodes. We show that a doomsday à la little sibling of the big rip is compatible with an accelerating universe, indeed at present it would mimic perfectly a ΛCDM scenario. It turns out that, even though the event seems to be harmless as it takes place in the infinite future, the bound structures in the universe would be unavoidably destroyed on a finite cosmic time from now. The model can be motivated by considering that the weak energy condition should not be strongly violated in our universe, and it could give us some hints about the status of recently formulated nonlinear energy conditions. [ABSTRACT FROM AUTHOR]

We present and develop several nonlinear energy conditions suitable for use in the semiclassical regime. In particular, we consider the recently formulated “flux energy condition” (FEC), and the novel “trace-of-square” (TOSEC) and “determinant” (DETEC) energy conditions. As we shall show, these nonlinear energy conditions behave much better than the classical linear energy conditions in the presence of semiclassical quantum effects. Moreover, whereas the quantum extensions of these nonlinear energy conditions seem to be quite widely satisfied as one enters the quantum realm, at least for quantum vacuum states, analogous quantum extensions are generally not useful for the linear classical energy conditions. [ABSTRACT FROM AUTHOR]

Massive gravity is a theory which has a tremendous amount of freedom to describe different cosmologies, but at the same time, the various solutions one encounters must fulfil some rather nontrivial constraints. Most of the freedom comes not from the Lagrangian, which contains only a small number of free parameters (typically three depending on counting conventions), but from the fact that one is in principle free to choose the reference metric almost arbitrarily--which effectively introduces a non-denumerable infinity of free parameters. In the current paper, we stress that although changing the reference metric would lead to a different cosmological model, this does not mean that the dynamics of the universe can be entirely divorced from its matter content. That is, while the choice of reference metric certainly influences the evolution of the physically observable foreground metric, the effect of matter cannot be neglected. Indeed the interplay between matter and geometry can be significantly changed in some specific models; effectively since the graviton would be able to curve the spacetime by itself, without the need of matter. Thus, even the set of vacuum solutions for massive gravity can have significant structure. In some cases, the effect of the reference metric could be so strong that no conceivable material content would be able to drastically affect the cosmological evolution. [ABSTRACT FROM AUTHOR]

We discuss the subtle relationship between massive gravity and bimetric gravity, focusing particularly on the manner in which massive gravity may be viewed as a suitable limit of bimetric gravity. The limiting procedure is more delicate than currently appreciated. Specifically, this limiting procedure should not unnecessarily constrain the background metric, which must be externally specified by the theory of massive gravity itself. The fact that in bimetric theories one always has two sets of metric equations of motion continues to have an effect even in themassive gravity limit, leading to additional constraints besides the one set of equations of motion naively expected. Thus, since solutions of bimetric gravity in the limit of vanishing kinetic term are also solutions of massive gravity, but the contrary statement is not necessarily true, there is no complete continuity in the parameter space of the theory. In particular, we study themassive cosmological solutions which are continuous in the parameter space, showing that many interesting cosmologies belong to this class. [ABSTRACT FROM AUTHOR]

Although it has been believed that models with generalized Chaplygin gas (GCG) do not contain singularities, in previous work we have studied how a big freeze could take place in some kinds of phantom-generalized Chaplygin gas. In the present work, we study some types of generalized Chaplygin gas in order to show how different sorts of singularities could appear in such models, either in the future or in the past. We point out that (i) singularities may not originate from the phantom nature of the fluid, and (ii) if initially the tension of the brane in a brane-world Chaplygin model is large enough, then an infrared cutoff appears in the past. [ABSTRACT FROM AUTHOR]

Abstract: This paper contains a detailed discussion on new cosmic solutions describing the early and late evolution of a universe that is filled with a kind of dark energy that may or may not satisfy the energy conditions. The main distinctive property of the resulting space–times is that they make to appear twice the single singular events predicted by the corresponding quintessential (phantom) models in a manner which can be made symmetric with respect to the origin of cosmic time. Thus, big bang and big rip singularity are shown to take place twice, one on the positive branch of time and the other on the negative one. We have also considered 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. [Copyright &y& Elsevier]