International Journal of Modern Physics D

We assume that Type Ia supernovae (SNe Ia) are standard candles which one could use to test cosmological theories. The Hubble Space Telescope team analyzed 186 SNe Ia¹ to test the standard cosmological model (SC) associated with expanded lengths in the universe and evaluate its parameters. We use the same sample to determine parameters of the conformal cosmological model (CC) with relative reference units of intervals, so that conformal quantities of general relativity are interpreted as observables. We concluded, that the test is extremely useful and allows the evaluation of the parameters of the model. From a formal statistical point of view the best-fit of the CC model is almost the same quality approximation as the best-fit of the SC model with Ω_Λ = 0.72, Ω_m = 0.28. As it was noted earlier, for CC models, a rigid matter component could substitute the Λ-term (or quintessence) existing in the SC model. We note that a free massless scalar field can generate such a rigid matter. We describe the results of our analysis for more recent "gold" data (for 192 SNe Ia).

The relativistic equations governing the non-adiabatic shear-free collapse of massive superdense stars in the presence of dissipative forces producing heat flow in the background of space–times of the Vaidya–Tikekar ansatz with associated physical three-spaces that have the three-spheroidal geometry are formulated. It is shown how the system can be used to examine the development and progress of the collapse during subsequent epochs until the radiating star becomes a black hole.

In this paper, inspired by the investigations on the theory of cosmological perturbations in Hořava–Lifshitz cosmology, we calculate the spectrum of primordial perturbation lead by a modified dispersion relation in proper time ω_pro ~ k^z/a^p in power-law expansion/contraction background a ~ tⁿ · z is the critical exponent and p is not necessarily equal to z · p = z is well-motivated by Hořava–Lifshitz gravity, and the cases with p ≠ z are generalizations beyond the scope. We discuss that for fixed z, if the spectrum is required to be scale-invariant, how should p depend on n. We conclude that there is always room for parameters for the generation of scale-invariant spectrum.

We construct a framework within which a mathematically precise, fully covariant, and exact averaging procedure for tensor fields on a manifold can be formulated. In particular, we introduce the Weitzenböck connection for parallel transport and argue that, within the context of averaging, frames and connections are the natural geometrical objects on the manifold.

We present a method to calculate the gravitational energy when asymptotic boundary conditions for the space–time are not given. This is the situation for most of the cosmological models. The expression for the gravitational energy is obtained in the context of the teleparallel equivalent of general relativity. We apply our method first to the Schwarzschild–de Sitter solution of Einstein's equation, and then to the Robertson–Walker universe. We show that in the first case our method leads to an average energy density of the vacuum space–time, and in the latter case the energy vanishes in the case of null curvature.

We construct and compare in this work a variety of simple models for strange stars, namely, hypothetical self-bound objects made of a cold stable version of the quark-gluon plasma. Exact, quasi-exact and numerical models are examined to find the most economical description for these objects. A simple and successful parametrization of them is given in terms of the central density, and the differences among the models are explicitly shown and discussed. In particular, we present a model starting with a Gaussian ansatz for the density profile that provides a very accurate and almost complete analytical integration of the problem, modulo a small difference for one of the metric potentials.

Spatially homogeneous and anisotropic Bianchi type VI₀ cosmological models with cosmological constant are investigated in the presence of anisotropic dark energy. We examine the effects of electromagnetic field on the dynamics of the universe and anisotropic behavior of dark energy. The law of variation of the mean Hubble parameter is used to find exact solutions of the Einstein field equations. We find that electromagnetic field promotes anisotropic behavior of dark energy which becomes isotropic for future evolution. It is concluded that the isotropic behavior of the universe model is seen even in the presence of electromagnetic field and anisotropic fluid.

Recently Hod proposed a lower bound on the relaxation time of a perturbed thermodynamic system. For gravitational systems this bound transforms into a condition on the fundamental quasinormal frequency. We test the bound in some space–times whose quasinormal frequencies are calculated exactly, as the three-dimensional BTZ black hole, the D-dimensional de Sitter space–time, and the D-dimensional Nariai space–time. We find that for some of these space–times their fundamental quasinormal frequencies do not satisfy the bound proposed by Hod.

Motivated by our recent work,⁷² we generalize this work to the interacting non-flat case. Therefore in this paper we deal with canonical, phantom and quintom models, with various fields that are non-minimally coupled to gravity, within the framework of interacting holographic dark energy. We employ the holographic model of interacting dark energy to obtain the equation of state for the holographic energy density in non-flat (closed) universe enclosed by the event horizon measured from the sphere of horizon named L.

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.