International Journal of Modern Physics D

The purpose of this paper is to study braneworld cosmologies in the presence of stringy corrections coupled to a canonical scalar field. Two independent models are explored which in their own right provide cosmologies exhibiting the present cosmic acceleration of the universe. The evolution of the cosmological scale factor is studied in four and ten-dimensional space–times. The four-dimensional model is preformed in the context of the nonminimal Maxwell–Gauss–Bonnet gravity while the ten-dimensional model is constructed from the implications of Kaluza–Klein cosmology together with the Gauss–Bonnet Lagrangian in the action with matter fields nonminimally coupled to gravity. Both the low energy and high energy limits are discussed for the two models and many interesting features are described in some detail.

Independently developed orbit determination software is employed to analyze the orbits of Pioneer 10 and 11 using Doppler data. The analysis takes into account the gravitational fields of the Sun and planets using the latest JPL ephemerides, accurate station locations, signal propagation delays (e.g. the Shapiro delay, atmospheric effects), the spacecraft's spin, and maneuvers. New to this analysis is the ability to utilize telemetry data for spin, maneuvers, and other on-board systematic effects. Using data that were analyzed in prior JPL studies,^1,2 the anomalous acceleration of the two spacecraft is confirmed. We are also able to put limits on any secondary acceleration (i.e. jerk) terms. The tools that were developed will be used in the upcoming analysis of recently recovered Pioneer 10 and 11 Doppler data files.

In the context of theories of the Kaluza–Klein type, with a large extra dimension, we study self-similar cosmological models in 5D that are homogeneous, anisotropic and spatially flat. The "ladder" to go between the physics in 5D and in 4D is provided by Campbell–Maagard's embedding theorems. We show that the 5D field equations R_AB = 0 determine the form of the similarity variable. There are three different possibilities: homothetic, conformal and "wavelike" solutions in 5D. We derive the most general homothetic and conformal solutions to the 5D field equations. They require the extra dimension to be spacelike, and are given in terms of one arbitrary function of the similarity variable and three parameters. The Riemann tensor in 5D is not zero, except in the isotropic limit, which corresponds to the case where the parameters are equal to each other. The solutions can be used as 5D embeddings for a great variety of 4D homogeneous cosmological models, with and without matter, including the Kasner universe. Since the extra dimension is spacelike, the 5D solutions are invariant under the exchange of spatial coordinates. Therefore they also embed a family of spatially inhomogeneous models in 4D. We show that these models can be interpreted as vacuum solutions in braneworld theory. Our work (I) generalizes the 5D embeddings used for FLRW models; (II) shows that anisotropic cosmologies are, in general, curved in 5D, in contrast with FLRW models, which can always be embedded in a 5D Riemann-flat (Minkowski) manifold; and (III) reveals that anisotropic cosmologies can be curved and devoid of matter, both in 5D and in 4D, even when the metric in 5D explicitly depends on the extra coordinate, which is quite different from the isotropic case.

The Bousso entropy bound is investigated for static, spherically symmetric configurations of an ideal gas with a Bose–Einstein or Fermi–Dirac distribution function. Gas of massive particles is considered. This paper is continuation of the previous work concerning the massless case. Special attention is devoted to light sheets generated by spheres. Conditions under which the Bousso bound can be violated are discussed and it is shown that a possible violating region cannot be arbitrarily large and that it is contained inside a sphere of unit Planck radius if the number of independent spin states g_s is small enough. It is also shown that the central temperature must exceed the Planck temperature in order to get a violation of the Bousso bound for g_s which is not too large. The situation for higher-dimensional space–times is also discussed and the conditions of Flanagan, Marolf and Wald are investigated.

Exact solutions to the Einstein field equations with cosmic string and a space-varying cosmological constant, viz. Λ = Λ(r), in the energy–momentum tensors are presented. Three cases have been studied: the variable cosmological constant (1) has power law dependence, (2) is proportional to the string fluid density, and (3) is purely a constant. Some cases of interesting physical consequences have been found where (i) the variable cosmological constant can be represented by a power law of the type Λ = 3r^-2, (ii) the variable cosmological constant and the cosmic string density are interdependent according to the relation Λ = -8πρ_s, and (iii) the cosmic string density can be scaled by a power law of the type ρ_s = r^-2. It is also shown that several known solutions can be recovered from the general form of the solutions obtained here.

The quantum effective Yang–Mills condensate (YMC) dark energy model has some distinctive features so that it naturally solves the coincidence problem and, at the same time, is able to give an equation of state w crossing -1. In this work we further employ the statefinder pair (r,s), introduced by Sahni et al., to diagnose the YMC model for three cases: the noncoupling, the YMC decaying into matter only, and the YMC decaying into both matter and radiation. The trajectories (r,s) and (r,q), and the evolutions r(z) and s(z), are explicitly presented. It is found that the YMC model in all three cases has r ≃ 1 for z < 10 and s ≃ 0 for z < 5 with only small deviations, ≃ 0.02, quite close to the cosmological constant model (LCDM), but is obviously differentiated from other dark energy models, such as quiessence or kinessence.

The Eddington Lagrangian in the purely affine formulation of general relativity generates the Einstein equations with the cosmological constant. The Ferraris–Kijowski purely affine Lagrangian for the electromagnetic field, which has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the Einstein–Maxwell Lagrangian in the metric formulation. We show that the sum of the two affine Lagrangians is dynamically inequivalent to the sum of the analogous Lagrangians in the metric–affine/metric formulation. We also show that such a construction is valid only for weak electromagnetic fields. Therefore the purely affine formulation that combines gravitation, electromagnetism and the cosmological constant cannot be a simple sum of terms corresponding to separate fields. Consequently, this formulation of electromagnetism seems to be unphysical, unlike the purely metric and metric–affine pictures, unless the electromagnetic field couples to the cosmological constant.

A recently formulated universal lower bound to the characteristic relaxation times of perturbed thermodynamic systems, derived from quantum information theory and (classical) thermodynamics and known to be saturated for (certain) black holes, is investigated in the light of the gravity–thermodynamics connection. A statistical-mechanical property, unrelated to gravity, essential for the validity of the generalized covariant entropy bound, namely the existence of a lower-limiting value l* for the size of thermodynamic systems, is found to provide a way to understand this universal relaxation bound, thus regardless of the kind of foundations (i.e. whether conventional or information-based) of the statistical-mechanical description. As a by-product an example of a conventional system (i.e. not a black hole) seemingly saturating the universal relaxation bound is provided.

In this paper the first exact interior solution to Einstein's field equations for a static and nonuniform braneworld star with local and nonlocal bulk terms is presented. It is shown that the bulk Weyl scalar is always negative inside the stellar distribution, and in consequence it reduces both the effective density and the effective pressure. It is found that the anisotropy generated by bulk gravity effect has an acceptable physical behavior inside the distribution. Using a Reissner–Nördstrom-like exterior solution, the effects of bulk gravity on pressure and density are found through matching conditions.

This paper proposes a class of nonstationary de Sitter, rotating and nonrotating, solutions to Einstein's field equations with a cosmological term of variable function Λ*(u). It is found that the space–time of the rotating nonstationary de Sitter model is algebraically special in the Petrov classification of the gravitational field with a null vector, which is a geodesic, shear-free, expanding as well as nonzero twist. However, that of the nonrotating nonstationary model is conformally flat, with nonempty space.

In this paper, the cosmology of the late and future universe is obtained from f(R) gravity with nonlinear curvature terms R² and R³ (R is the Ricci scalar curvature). It is different from f(R) dark energy models where nonlinear curvature terms are taken as a gravitational alternative to dark energy. In the present model, neither linear nor nonlinear curvature terms are taken as dark energy. Rather, dark energy terms are induced by curvature terms and appear in the Friedmann equation derived from f(R) gravitational equations. This approach has an advantage over f(R) dark energy models in three ways: (i) results are consistent with WMAP observations, (ii) dark matter is produced from the gravitational sector and (iii) the universe expands as ~ t^2/3 during dominance of the curvature-induced dark matter, which is consistent with the standard cosmology. Curvature-induced dark energy mimics phantom and causes late acceleration. It is found that transition from matter-driven deceleration to acceleration takes place at the redshift 0.36 at time 0.59 t₀ (t₀ is the present age of the universe). Different phases of this model, including acceleration and deceleration during the phantom phase, are investigated. It is found that expansion of the universe will stop at the age of 3.87 t₀ + 694.4 kyr. After this epoch, the universe will contract and collapse by the time of 336.87 t₀ + 694.4 kyr. Further, it is shown that cosmic collapse obtained from classical mechanics can be avoided by making quantum gravity corrections relevant near the collapse time due to extremely high energy density and large curvature analogous to the state of the very early universe. Interestingly, the cosmological constant is also induced here; it is extremely small in the classical domain but becomes very high in the quantum domain. This result explains the largeness of the cosmological constant in the early universe due to quantum gravity effects during this era and its very low value in the present universe due to negligible quantum effect in the late universe.