International Journal of Geometric Methods in Modern Physics

In this paper, we show that thermodynamics is sensitive to the existence of a fundamental spin tensor. In general, the thermodynamics is not invariant by a change of the stress-energy tensor of a fundamental quantum field with a divergence transformation leaving the total energy, momentum and angular momentum unchanged. Among the quantities which are changed by such a transformation, there are densities at equilibrium with rotation and nonequilibrium ones like transport coefficients and total entropy. Therefore, at least in principle, it could be possible to probe the existence of a spin tensor, with major consequences for general relativistic theories, with a thermodynamics experiment.

We shall consider possible potentials emerging in (purely metric) f(R)-theories for the conformal scalar field. We shall discuss possible approaches to determine models with specific potentials and show that some potentials qualitatively similar to the typical Higgs potentials are allowed.

The weak cosmic censorship conjecture is a central open problem in classical general relativity. Under the assumption of spherical symmetry, Christodoulou has investigated the conjecture for two different matter models; a scalar field and dust. He has shown that the conjecture holds true for a scalar field but that it is violated in the case of dust. The outcome of the conjecture is thus sensitive to which model is chosen to describe matter. Neither a scalar field nor dust are realistic matter models. Collisionless matter, or Vlasov matter, is a simple matter model but can be considered to be realistic in the sense that it is used by astrophysicists. The present status on the weak cosmic censorship conjecture for the Einstein–Vlasov system is reviewed here.

We examine an extension of General Relativity with an explicit non-minimal coupling between matter and curvature. The purpose of this work is to present an overview of the implications of the latter to various contexts, ranging from astrophysical matter distributions to a cosmological setting. Various results are discussed, including the impact of this non-minimal coupling on the choice of Lagrangian density, on a mechanism to mimic galactic and cluster dark matter, on the possibility of accounting for the accelerated expansion of the Universe, energy density fluctuations and modifications to post-inflationary reheating. The equivalence between a model exhibiting a non-minimal coupling and multi-scalar-theories is also discussed.

We summarize the use of Noether symmetries in Minisuperspace Quantum Cosmology. In particular, we consider minisuperspace models, showing that the existence of conserved quantities gives selection rules that allow to recover classical behaviors in cosmic evolution according to the so-called Hartle criterion. Such a criterion selects correlated regions in the configuration space of dynamical variables whose meaning is related to the emergence of classical observable universes. Some minisuperspace models are worked out starting from Extended Gravity, in particular coming from scalar-tensor, f(R) and f(T) theories. Exact cosmological solutions are derived.

In this work, two systems are analyzed within the framework of the relativistic Boltzmann equation. One of them refers to a description of binary mixtures of electrons and protons and of electrons and photons subjected to external electromagnetic fields in special relativity. In this case the Fourier and Ohm laws are derived and the corresponding transport coefficients are obtained. In the other a relativistic gas under the influence of the Schwarzschild metric is studied. It is shown that the heat flux in Fourier's law in the presence of gravitational fields has three contributions, the usual dependence on the temperature gradient, and two relativistic contributions, one of them associated with an acceleration and another to a gravitational potential gradient. Furthermore, it is shown that the transport coefficient of thermal conductivity decreases in the presence of a gravitational field. The dependence of the temperature field in the presence of a gravitational potential is also discussed.

We consider modified gravity which may describe the early-time inflation and/or late-time cosmic acceleration of the universe. In particular, we discuss the properties of F(R), F(G), string-inspired and scalar-Einstein–Gauss–Bonnet gravities, including their FRW equations and fluid or scalar-tensor description. Simplest accelerating cosmologies are investigated and possibility of unified description of the inflation with dark energy is described. The cosmological reconstruction program which permits to get the requested universe evolution from modified gravity is developed. As some extension, massive F(R) bigravity which is ghost-free theory is presented. Its scalar-tensor form turns out to be the easiest formulation. The cosmological reconstruction method for such bigravity is presented. The unified description of inflation with dark energy in F(R) bigravity turns out to be possible.

There is compelling evidence, nowadays, that the present expansion of the Universe is accelerated. In Einstein gravity this acceleration is explained by invoking some exotic energy component with a huge negative pressure. More general gravity theories simply modify the Einstein–Hilbert action in ad hoc manner. Here, we show that whatever its origin, this acceleration is consistent with the second law of thermodynamics in the sense that the entropy of the causal cosmic horizon plus that of matter and fields inside it must never decrease and it should approach a finite maximum in the long run. In this light, the acceleration could have been anticipated on thermodynamic grounds well before its actual discovery.

Inflationary models are characterized by the form of a potential which is arbitrary and usually parametrized so as to match the observational data. However, making use of the renormalization group methods to a gravity-scalar field system it is possible to find physically nontrivial potentials that might be relevant for cosmology and particle physics as well. I will pinpoint the way this class of potentials may be found as well as discuss their utility for inflationary models.

The false (unstable) vacuum is discussed from the point of view of the quantum theory of unstable states. Properties of the energy of the system in the unstable vacuum state are studied. Within the model considered, it is shown that at very late times, the energy of the system in the false vacuum state tends to the energy of the system in the true vacuum state as 1/t².

We provide a brief summary of the history of galaxy structure studies. We also introduce several large-scale redshift surveys and summarize the most commonly used methods to identify the groups and clusters of galaxies. We present several catalogs of galaxy groups. These catalogs can be used to study the galaxy groups in different environments. We also consider the properties of superclusters of galaxies in the nearby universe and describe the largest system of galaxies observed — the Sloan Great Wall.

Every story has two sides and so does any good equation. Recent developments in observational cosmology have led to attempts to make modifications on both sides of the Einstein equation to explain some of the puzzling new findings. The work described here is concerned with an examination of the source of gravity that we usually find on the right-hand side of Einstein's equation. My aim is to describe a modified version of the stress-energy tensor that is the source of the gravitational field. The derivation is based on the kinetic theory of a gas of identical particles with no internal structure. The presentation here is in two parts. In Part I, I describe the stress tensor that Xinzhong Chen and I have proposed for the matter tensor for a nonrelativistic gas with input from Hongling Rao and Jean-Luc Thiffeault. Our derivation of the equations of fluid dynamics is based on kinetic theory and without recourse to the standard Chapman–Enskog approximation. The nonrelativistic treatment reveals the underlying physics clearly and it facilitates comparison with experimental results on acoustic propagation. Further, it provides a setting for a Newtonian cosmology, which remains a topic of some interest. I regret though that there is room only for the relativistic version of cosmology here. In Part II, I derive the stress-energy tensor in the relativistic case in a similar manner and exhibit its application to the usual isotropic cosmological model. The surprising result of that discussion is that, in addition to the Friedmann solution, we find a second solution that arises from terms that the usual Chapman–Enskog approximation discards. The new solution is a temporal analogue of a spatial shock wave. Just as the usual shock waves make transitions in properties within a mean free path, the new solution can change its properties in a mean flight time. Whereas the Friedmann solution is not dissipative, the new solution produces entropy at a rate that may be of cosmological interest. For the calculation of cosmic entropy production I work in the ultrarelativistic limit in which particle masses are negligible. A stability calculation to decide whether and when the new solution may be realized has yet to be done since the microphysics seems so uncertain.

We study the Scalar Field Cosmology (SFC) using the geometric language of the phase space. We define and study an ensemble of dynamical systems as a Banach space with a Sobolev metric. The metric in the ensemble is used to measure a distance between different models. We point out the advantages of visualization of dynamics in the phase space. It is investigated the genericity of some class of models in the context of fine tuning of the form of the potential function in the ensemble of SFC. We also study the symmetries of dynamical systems of SFC by searching for their exact solutions. In this context, we stressed the importance of scaling solutions. It is demonstrated that scaling solutions in the phase space are represented by unstable separatrices of the saddle points. Only critical point itself located on two-dimensional stable submanifold can be identified as scaling solution. We have also found a class of potentials of the scalar fields forced by the symmetry of differential equation describing the evolution of the Universe. A class of potentials forced by scaling (homology) symmetries was given. We point out the role of the notion of a structural stability in the context of the problem of indetermination of the potential form of the SFC. We characterize also the class of potentials which reproduces the ΛCDM model, which is known to be structurally stable. We show that the structural stability issue can be effectively used is selection of the scalar field potential function. This enables us to characterize a structurally stable and therefore a generic class of SFC models. We have found a nonempty and dense subset of structurally stable models. We show that these models possess symmetry of homology.

We discuss bulk viscous cosmological models. Since the bulk viscous pressure is negative, viable viscous cosmological scenarios with late time accelerated expansion can in principle be constructed. After discussing some alternative models based on bulk viscous effects we will focus on a model very similar to the standard ΛvCDM. We argue that a ΛvCDM model, where we assign a very small (albeit perceptible) bulk viscosity to dark matter is in agreement with available cosmological observations. Hence, we work with the concept of viscous Cold Dark Matter (vCDM). At the level of the perturbations, the growth of vCDM structures is slightly suppressed when compared with the standard CDM ones. Having in mind that the small scale problems of the ΛCDM model are related to an excess of clustering, our proposal seems to indicate a possible direction for solving the serious drawbacks of the CDM paradigm within the standard cosmological model.

Interactions inside the cosmological dark sector influence the cosmological dynamics. As a consequence, the future evolution of the Universe may be different from that predicted by the ΛCDM model. We review main features of several recently studied models with nongravitational couplings between dark matter and dark energy.