Vaidya black hole in non-stationary de Sitter space: Hawking’s temperature

In this paper we present a class of non-stationary solutions of Einstein’s field equations describing embedded Vaidya-de Sitter black holes with a cosmological variable function Λ(u). The Vaidya-de Sitter black hole is interpreted as the radiating Vaidya black hole is embedded into the non-stationary de Sitter space with variable Λ(u). The energy-momentum tensor of the Vaidya-de Sitter black hole is expressed as the sum of the energy-momentum tensors of the Vaidya null fluid and that of the non-stationary de Sitter field, and satisfies the energy conservation law. We study the energy conditions (like weak, strong and dominant conditions) for the energy-momentum tensor. We find the violation of the strong energy condition due to the negative pressure and leading to a repulsive gravitational force of the matter field associated with Λ(u) in the space-time. We also find that the time-like vector field for an observer in the Vaidya-de Sitter space is expanding, accelerating, shearing and non-rotating. It is also found that the space-time geometry of non-stationary Vaidya-de Sitter solution with variable Λ(u) is Petrov type D in the classification of space-times. We also find the Vaidya-de Sitter black hole radiating with a thermal temperature proportional to the surface gravity and entropy also proportional to the area of the cosmological black hole horizon.     

Variable cosmological “constant” and motion of a test particle in a cloud of dust

We find that Einstein’s like field equations with coordinate-dependent cosmological “constant” Λ(x ⁱ ) imply a non geodesic law of motion for test particles moving in a continuous distribution of incoherent matter (“dust”). The deviation from the geodesic law depends on the derivatives ?Λ/? x ⁱ and, in the weak field approximation, causes an anomalous acceleration A～(Vc ²/γ ρ)?Λ/? t+(c ⁴/γ ρ)?Λ/? r where V=dr/dt, c=the speed of light, γ=8π G with G=the gravitational coupling, ρ=the mass density of the cloud, r and t are the radial and time coordinate respectively. Reasonable assumptions on Λ=Λ(t) give A<10^?8 cm/s² when ρ>10^?29 g/cm³ i.e. in all known astrophysical systems. A possible connection with the anomalous Pioneer acceleration is shortly discussed in the case of a cosmological “constant” coupled to matter.     

Cosmological deductions from the relativistic stability of clusters of galaxies

Clusters of galaxies are approximated by the Schwarzschild interior solution (with non-zero cosmological constant) embedded in a Robertson/Walker background. The conditions that the two metrics join up smoothly and that the cluster be stable imply either (a)k=?1 with Λ lying in the range ?1.1×10^?27?Λ?1.5×10^?36 (s^?2), or (b)k=0. Also, superclustering on a scale larger than 0.5 Mpc is unacceptable unless Λ<0.     

General class of Bianchi cosmological models with Λ in creation-field cosmology

The solutions of Einstein’s equations with cosmological constant (Λ) in the presence of a creation field have been obtained for general class of anisotropic cosmological models. We have obtained the cosmological solutions for two different scenarios of average scale factor. In first case, we have discussed three different types of physically viable cosmological solutions of average scale factor for the general class of Bianchi cosmological models by using a special law for deceleration parameter which is linear in time with a negative slope. In second case, we have discussed another three different forms of cosmological solutions by using the average scale factor in three different scenarios like Intermediate scenario, Logamediate scenario and Emergent scenario. All physical parameters are calculated and discussed in each physical viable cosmological model. We examine the nature of creation field and cosmological constant is dominated the early Universe but they do not survive for long time and finally tends to zero for large cosmic time t. We have also discussed the all energy conditions in each cases.     

Zel’dovich Λ and Weinberg’s relation: an explanation for the cosmological coincidences

In 1937 Dirac proposed the large number hypothesis (LNH). The idea was to explain that these numbers were large because the Universe is old. A time variation of certain “constants” was assumed. So far, no experimental evidence has significantly supported this time variation. Here we present a simplified cosmological model. We propose a new cosmological system of units, including a cosmological Planck’s constant that “absorbs” the well known large number 10¹²⁰. With this new Planck’s constant no large numbers appear at the cosmological level. They appear at lower levels, e.g. at the quantum world. We note here that Zel’dovich formula, for the cosmological constant Λ, is equivalent to the Weinberg’s relation. The immediate conclusion is that the speed of light c must be proportional to the Hubble parameter H, and therefore decrease with time. We find that the gravitational radius of the Universe and its size are one and the same constant (Mach’s principle). The usual cosmological Ω’s parameters for mass, lambda and curvature turn out to be all constants of order one. The anthropic principle is not necessary in this theory. It is shown that a factor of 10⁶¹ converts in this theory a Planck fluctuation (a quantum black hole) into a cosmological quantum black hole: the Universe today. General relativity and quantum mechanics give the same local solution of an expanding Universe with the law a(t)≈const?t. This constant is just the speed of light today. Then the Hubble parameter is exactly H=a(t)′/a(t)=1/t.     

Bianchi VI h with variable gravitational and cosmological constants

In order to study how the gravitational and the cosmological constants, G, Λ may vary, we consider two theoretical frameworks which are, a modification of the General Relativity and several scalar models (the standard, non-interacting and interacting models and their respective modifications to allow a G varying). We find exact self-similar solutions for the geometry Bianchi VI _h , (that is, the models: III, VI₀, and VI _h ,). Some physical and geometrical properties of the models are also discussed and we compare the obtained theoretical results with the current observational data. In the first of the theoretical models, we reach the conclusion that, from the structure of the field equations, the behaviour of Λ and G are related, but taking into account the observational data, we conclude that the Λ behaves as a positive decreasing time function while G is growing but in the long time regimen it tends to a constant value. In the scalar models, our solutions predict a “positive” dynamical cosmological constant in all the obtained solutions while the behaviour of G yields indeterminate, since its depends on a free parameter, G≈t ^2α , so it may be growing or decreasing as in the scalar-tensor theories.     

Cosmological dynamics of EDGP model with a tachyon field on the brane

We consider the cosmological dynamics of a tachyon field localized on the extended DGP braneworld scenario. We present a detailed analysis of the critical points in the phase space of the model, their stability and late-time cosmological viability of the solutions. We study the luminosity distance behavior of this ?EDGP model and compare it with ΛCDM model. Also we show that the EDGP solutions in the presence of tachyon field can explain late time acceleration of the universe.     

Measuring ΩM and ΩΛ with long‐duration gamma‐ray bursts

Gamma‐ray bursts (GRBs) are one of the most luminous events in the Universe. In addition, the Universe itself is almost transparent to γ ‐rays, making GRBs detectable up to very high redshifts. As a result, GRBs are very suitable to probe the cosmological parameters. This work shows the potential of long‐duration GRBs for measuring the cosmological parameters Ω_M and Ω_Λ by comparing the observed log N ‐log P distribution with the theoretical one. Provided that the GRBs rate and luminosity function are well determined, the best values and 1σ confidence intervals obtained are Ω_M = 0.22^+0.05_–0.03 and Ω_Λ = 1.06^+0.05_–0.10. Finally, a set of simulations show the ability of the method to measure Ω_M and Ω_Λ (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamics of charged shell with a cosmological constant

Using the Darmois–Israel formalism technique, charged thin shell in the presence of a cosmological constant is constructed. An equation governing the behavior of the radial pressure across the junction surface is deduced. The cosmological constant term and the charge term slows down the collapse of matter.The spherical N-shell model with an appropriate initial condition imitates quite well the FRW universe with Λ ≠ 0.     

Relativistic anisotropic charged fluid spheres with varying cosmological constant

Static spherically symmetric anisotropic source has been studied for the Einstein-Maxwell field equations assuming the erstwhile cosmological constant Λ to be a space-variable scalar, viz., Λ=Λ(r). Two cases are examined out of which one reduces to isotropic sphere. The solutions thus obtained are shown to be electromagnetic in origin as a particular case. It is also shown that the generally used pure charge condition, viz., ρ+p=0 is not always required for constructing electromagnetic mass models.     

Power spectrum distortions in CMB map one-dimensional cross-sections depending on the cosmological model. II

We examine the effect produced by the variation of cosmological parameters on the power spectra of one-dimensional cross-sections of the cosmic microwave background maps in a narrow range of spatial frequencies. Variation of the Ω _b and Ω_Λ density parameters has little effect on the power spectrum deviation from the one expected within the ΛCDM model. At the same time, variations in the spectral index of primordial fluctuations significantly affect the amplitude of the power spectrum of one-dimensional cross-sections. We observe a lack of signal generated by the even harmonics in the ILC map as compared with model expectations.     

Exact self-similar Bianchi II solutions for some scalar-tensor theories

We study how may behave the gravitational and the cosmological “constants”, (G and Λ) in several scalar-tensor theories with Bianchi II symmetries. By working under the hypothesis of self-similarity we find exact solutions for three different theoretical models, which are: the Jordan-Brans-Dicke (JBD) with Λ(?), the usual JBD model with potential U(?) (that mimics the behavior of Λ(?)) and the induced gravity (IG) model proposed by Sakharov and Zee. After a careful study of the obtained solutions we may conclude that the solutions are quite similar although the IG model shows some peculiarities.     

The gas mass fraction in local and Z > 0.7 Galaxy Clusters: constraints on Cosmology

We present a study of the baryonic fraction in galaxy clusters aimed at constraining the cosmological parameters Ω_m, Ω_Lgr; and the ratio between the pressure and density of the `dark' energy, w. We use results on the gravitating mass profiles of a sample of nearby galaxy clusters observed with the BeppoSAX X-ray satellite (Ettori, De Grandi and Molendi, 2002)to set constraints on the dynamical estimate of Ω_m. We then analyze Chandra observations of a sample of eight distant clusters with redshift in the range 0.72 and 1.27 and evaluate the geometrical limits on the cosmological parameters Ω_m, Ω_Λ and w by requiring that the gas fraction remains constant with respect to the look-back time. By combining these two independent probability distributions and using a priori distributions on both Ω_b and H ₀ peaked around primordial nucleosynthesis and HST-Key Project results respectively, we obtain that, at 95.4 per cent level of confidence, (i) w < —0.54, (ii)Ω_m = 0.34^+0.11 _—0.05, Ω_Λ = 1.50^+0.24 _—1.13 for w = — 1 (corresponding to the case for a cosmological constant), and (iii) Ω_m = 1 —Ω_Λ = 0.33^+0.06 _—0.05 for a flat Universe. This paper summarizes the work in press at Astronomy & Astrophysics by Ettori, Tozzi and Rosati (astro-ph/0211335).     

The number of information bits related to the minimum quantum and gravitational masses in a vacuum dominated universe

Wesson obtained a limit on quantum and gravitational mass in the universe by combining the cosmological constant Λ, Planck’s constant ?, the speed of light c, and also the gravitational constant G. The corresponding masses are 2.0×10^?62 kg and 2.3×10⁵⁴ kg respectively, and in general can be obtained with the help of a generic dimensional analysis, or from an analysis where the cosmological constant appears in a four dimensional space-time and as a result of a higher dimensional reduction. In this paper our goal is to establish a relation for both quantum and gravitational mass as function of the information number bit N. For this reason, we first derive an expression for the cosmological constant as a function of information bit, since both masses depend on it, and then various resulting relations are explored, in relation to information number of bits N. Fractional information bits imply no information extraction is possible. We see, that the order of magnitude of the various parameters as well as their ratios involve the large number 10¹²², that is produced naturally from the fundamental parameters of modern cosmology. Finally, we propose that in a complete quantum gravity theory the idea of information the might have to be included, with the quantum bits of information (q-bits) as one of its fundamental parameters, resulting thus to a more complete understanding of the universe, its laws, and its evolution.     

WMAP-2006: Cosmological parameters and large-scale structure of the universe

The parameters of the cosmological model with cold dark matter and cosmological constant (ΛCDM model) were determined using three-year Wilkinson Microwave Anisotropy Probe observations of cosmic microwave background together with some data on the large-scale structure of the universe. The data cover scales from 1 to 10 000 Mpc. The best-fit ΛCDM model parameters were derived by minimizing the x ² statistic with the use of the Levenberg-Markquardt approach (Ω_Λ = 0.736 ± 0.065, Ω_m = 0.238 ± 0.080, Ω_b = 0.05 ± 0.011, h = 0.68 ± 0.09, σ₈ = 0.73 ± 0.08, and n _s = 0.96 ± 0.015). The ΛCDM model with these parameters is shown to agree well with the angular power spectrum of cosmic microwave background temperature fluctuations and with the density perturbation power spectra estimated from spatial distributions of galaxies and rich clusters of galaxies as well as from the statistics of the Ly _α absorption lines in the spectra of distant quasars. The accord between the model large-scale structure characteristics and the observed ones is analyzed, and conceivable factors causing appreciable discrepancies between some characteristics are discussed.     

The entropy-corrected holographic dark energy in Brans-Dicke cosmology with varying mass fermions

We aim in this paper to study Brans-Dicke cosmology in the presence of varying mass fermions and a self-interaction potential. Furthermore, we also probe the entropy corrected holographic dark energy (ECHDE) in the model in two non-interacting and interacting scenarios. The model parameters are constrained by using the recent SNe Ia observational data and tested against observational data of Hubble parameter. For a comparison, we also constrained and tested the cosmological parameters in ΛCDM model with the same observational data. We show that in non of the scenarios the model prediction is better than ΛCDM model.     

Effective dark energy models and dark energy models with bounce in frames of F(T) gravity

Various cosmological models in frames of F(T) gravity are considered. The general scheme of constructing effective dark energy models with various evolution is presented. It is showed that these models in principle are compatible with ΛCDM model. The dynamics of universe governed by F(T) gravity can mimics ΛCDM evolution in past but declines from it in a future. We also construct some dark energy models with the “real” (non-effective) equation-of-state parameter w such that w≤?1. It is showed that in F(T) gravity the Universe filled phantom field not necessarily ends its existence in singularity. There are two possible mechanisms permitting the final singularity. Firstly due to the nonlinear dependence between energy density and H ² (H is the Hubble parameter) the universe can expands not so fast as in the general relativity and in fact Little Rip regime take place instead Big Rip. We also considered the models with possible bounce in future. In these models the universe expansion can mimics the dynamics with future singularity but due to bounce in future universe begin contracts.     

Exploring the gamma ray horizon with the next generation of gamma ray telescopes. Part 1: Theoretical predictions

The physics potential of the next generation of gamma ray telescopes in exploring the gamma ray horizon is discussed. It is shown that a reduction in the gamma ray detection threshold might open a window to use precise determinations of the gamma ray horizon as a function of redshift to either put strong constraints on the extragalactic background light modelling or to obtain relevant independent constraints on the cosmological densities Ω_M and Ω_Λ.     

Entropy of viscous Universe models

The cosmological event horizon entropy and the apparent horizon entropy of the ΛCDM and the Bianchi type I Universe model with viscosity has been calculated numerically, and analytically in the large time limit. It is shown that for these Universe models the cosmological event horizon entropy increases with time and for large times it approaches a finite maximum value. The effect of viscosity upon the entropy is also studied and we have found that its role is to decrease the entropy. The bigger the viscosity coefficient is the less the entropy will be. Furthermore, the radiation entropy for the ΛCDM Universe model with and without viscosity is investigated, and together with the cosmological event horizon entropy are used to examine the validity of the generalized second law of thermodynamics, which states that the total rate of change of entropy of the Universe is never negative, in this Universe model.     

Bianchi type-I cosmological models with time dependent q and Λ-term in general relativity

On getting motivation from increasing evidence for the need of a geometry that resembles Bianchi morphology to explain the observed anisotropy in the WMAP data, Einstein’s field equations with variable cosmological “constant” are considered in presence of perfect fluid for a homogeneous and anisotropic Bianchi type-I space-time. Einstein’s field equations are solved by considering a time dependent deceleration parameter which affords a late time acceleration in the universe. The cosmological constant Λ is found to be a decreasing function of time and it approaches a small positive value at the present epoch which is corroborated by consequences from recent supernovae Ia observations. From recently developed Statefinder pair, the behavior of different stages of the evolution of the universe has been studied. The physical significance of the cosmological models have also been discussed.