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.     

Exact Brans-Dicke cosmologies with a cosmological constant

We present the general Brans-Dicke-Friedmann-Robertson-Walker (k=0) vacuum solutions with a cosmological constant. The space-times considered here are the generalizations of the de Sitter models of the general theory of relativity.     

Hawking radiation and entropy in de Sitter spacetime

Using the analytic extension method, we study Hawking radiation of an (n+4)-dimensional Schwarzschild-de Sitter black hole. Under the condition that the total energy is conserved, taking the reaction of the radiation of particles to the spacetime into consideration and considering the relation between the black hole event horizon and cosmological horizon, we obtain the radiation spectrum of de Sitter spacetime. This radiation spectrum is no longer a strictly pure thermal spectrum. It is related to the change of the Bekenstein-Hawking (B-H) entropy corresponding the black hole event horizon and cosmological horizon. The result satisfies the unitary principle. At the same time, we also testify that the entropy of de Sitter spacetime is the sum of the entropy of black hole event horizon and the one of cosmological horizon.     

Generalized de Sitter solution in multi-dimensional cosmology with static internal spaces

A multi-dimensional cosmological model with space-time consisting of n(n ≥ 2) Einstein spaces M_i is investigated in the presence of a cosmological constant λ and a homogeneous minimally coupled free scalar field. A generalized de Sitter solution was found for λ > 0 and a Ricci-flat external space for the case of static internal spaces with fine tuning of parameters.     

Phase transition in Schwarzschild-de Sitter spacetime

Using a static massive spherically symmetric scalar field coupled to gravity in the Schwarzschild-de Sitter (SdS) background, first we consider some asymptotic solutions near horizon and their local equations of state (E.O.S.) on them. We show that near cosmological and event horizons our scalar field behaves as a dust. At the next step near two pure de Sitter or Schwarzschild horizons we obtain a coupling dependent pressure to energy density ratio. In the case of a minimally coupling this ratio is ?1 which springs to the mind thermodynamical behavior of dark energy. If having a negative pressure behavior near these horizons we concluded that the coupling constant must be ξ<¼. Therefore we derive a new constraint on the value of our coupling ξ. These two different behaviors of unique matter in the distinct regions of spacetime at present era can be interpreted as a phase transition from dark matter to dark energy in the cosmic scales and construct a unified scenario.     

Black hole solutions in warped DGP brane world

Using the effective gravitational field equations in the warped DGP brane-world scenario (Maeda et al. in Phys. Rev. D 68:024033, 2003), we study spherically symmetric vacuum (static black hole) solutions on the brane. Working with a conformally flat bulk, we have obtained an exact Schwarzschild–de Sitter black hole solution similar to the standard solution in the presence of a cosmological constant, which confirms the idea that an extra term in the effective vacuum field equations on the warped DGP brane can play the role of a positive cosmological constant.     

A novel early dark energy model

We present a theoretical study of an early dark energy (EDE) model. The equation of state ω(z) evolves during the thermal history in a framework of a Friedmann-Lemaitre-Robertson-Walker Universe, following an effective parametrization that is a function of redshift z. We explore the evolution of the system from the radiation domination era to the late times, allowing the EDE model to have a non-negligible contribution at high redshift (as opposed to the cosmological constant that only plays a role once the structure is formed) with a very little input to the Big Bang Nucleosynthesis, and to do so, the equation of state mimics the radiation behaviour, but being subdominant in terms of its energy density. At late times, the equation of state of the dark energy model asymptotically tends to the fiducial value of the De Sitter domination epoch, providing an explanation for the accelerated expansion of the Universe at late times, emulating the effect of the cosmological constant. The proposed model has three free parameters, that we constrain using SNIa luminosity distances, along with the CMB shift parameter and the deceleration parameter calculated at the time of dark energy - matter equality. With full knowledge of the best fit for our model, we calculate different observables and compare these predictions with the standardΛCDM model. Besides the general consent of the community with the cosmological constant, there is no fundamental reason to choose that particular candidate as dark energy. Here, we open the opportunity to consider a more dynamical model, that also accounts for the late accelerated expansion of the Universe.     

De Sitter-invariant vacuum state and temperature green function

Using the method of canonical quantization in the static spacetime, we calculated the temperature Green function of the real scalar field of the de Sitter spacetime. We then used the generating functional of the Green function in the euclidean path integral representation to prove that the temperature Green function for $\text{T =}\text{(}\text{Λ}\text{3}\text{)}\text{2π}$, Λ being positive cosmological constant, is identical with the Green function G_E on the 4-dimensional euclidean sphere, thereby showing that the de Sitter-invariant vacuum state with respect to an inertial measuring system (geodesic observer) is the quantum mixed state with a Hawking temperature equal to T.     

Cosmological dynamics of a quintom field on the warped DGP brane

As a generalization of the Brans-Dicke type scalar-tensor gravity in a braneworld context, we study cosmological phase space of a braneworld model with induced gravity in the presence of a scalar field on the brane. We consider a quintom field minimally or non-minimally coupled to induced gravity on the warped DGP brane and we present a detailed analysis of the critical points, their stability and late-time cosmological viability of the solutions within a phase space approach. In particular, de Sitter solutions, different from the famous self-accelerated branch of the DGP model are found and the phase-space analysis for checking their attractor properties is performed. We analyze also the possibility of crossing of the phantom divide by the effective equation of state parameter of the model. We also focus on the classical stability of the solutions in w–w′ phase plane.     

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.     

The effect of a relative infinity on cosmological redshifts

We present anon-general relativistic cosmological model with the following features.

All cosmological objects appear to be receding from each other. There are two mathematically distinct types of objects.

Type I objects have apparent magnitudes and apparent angular diameters comparable to those for standard FLRW models. Their redshifts are bounded; this bound is at least 3.

Type II objects can have unlimited redshifts. They appear significantly smaller than Type I objects with the same redshift, and (for redshifts greater than 1) appear brighter (and more so for larger redshifts).

The model is an extension of classical de Sitter spacetime in which the location of infinity is allowed to be relative.     

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.     

Cosmological Parameters: Where are we?

The present-day large increase of the amount of data relevant to cosmology, as well as their increasing accuracy, leads to the idea that the determination of cosmological parameters has been achieved with a rather good precision, may be of the order of 10%. There is a large consensus around the so-called concordance model. Indeed this model does fit an impressive set of independent data, the most impressives been: CMB C_l curve, most current matter density estimations, Hubble constant estimation from HST, apparent acceleration of the Universe, good matching of the power spectrum of matter fluctuations. However, the necessary introduction of a non zero cosmological constant is an extraordinary new mystery for physics, or more exactly the come back of one of the ghost of modern physics since its introduction by Einstein. Here, I would like to emphasize that some results are established beyond reasonable doubt, like the (nearly) flatness of the universe and the existence of a dark non-baryonic component of the Universe. But also that the evidence for a positive cosmological constant may not be as strong as needed for its existence to be considered as established beyond doubt. In this respect, I will argue that an Einstein-De Sitter universe might still be a viable option. Some observations do not fit the concordance picture. I discuss several of the claimed observational evidences supporting the concordance model and will focus more specifically on the observational properties of clusters which offer powerful constraints on various quantities of cosmological interest. They are particularly interesting in constraining the cosmological density parameter, nicely complementing the CMB result, which by its own does not request a non vanishing cosmological constant, contrary to what is sometimes claimed. Early, local, estimations based on the M/L ratio are now superseded by new tests that have been proposed during the last ten years which are globalin nature. Here, I will briefly discuss three of them: 1) the evolution of the abundance of clusters with redshift 2) the baryon fraction measured in local clusters 3) apparent evolution of the baryon fraction with redshift. I will show that these three independent tests lead to high matter density for the Universe in the range 0.6 — 1. I therefore conclude that the dominance of vacuum to the various density contributions to the Universeis presently a fascinating possibility, but it is still premature to consider it as an established scientific fact.     

Scalar fields and the inflationary phase of the cosmic evolution

Scalar fields are an important ingredient of modern cosmological models describing the very early universe. If they are of the Higgs field type, scalar fields offer a possibility to understand why the cosmological constant is such a small quantity. This is because of the fact that different ground states are possible for a Higgs field. The unstable ground state gives an inflationary stage of the cosmic evolution and a large cosmological constant whereas the stable ground state has a vanishing cosmological constant and is decisive for the late time behaviour with an Einstein-De Sitter — like expansion law.     

Symbolic analytical developments of the zero pressure cosmological model of the universe

In the present paper, literal analytical solutions in power series forms are developed for the radius of curvature and the expansion velocity of the zero pressure cosmological models of the universe at any time t. Also, we develop literal analytical solutions in power series forms for the inverse problem of the zero pressure cosmological model, that is to find the time $t=\tilde{t}$ (say) at which the radius of curvature of the model $R=\tilde{R}$ (say) is known. The importance of these analytical power series representations is that, they are invariant under many operations because, addition, multiplication, exponent ion, integration, different ion, etc of a power series is also a power series. A fact which provides excellent flexibility in dealing with analytical as well as computational developments of the problems related to zero pressure cosmological models.For computational developments of these solutions, an efficient method using continued fraction theory is provided. By means of the present methods we able to analyze some known zero-pressure cosmological models, of these are Einstein and De Sitter models. In addition we also analyzed some other models by which one can know if the universe keep expanding forever, or will it reach a maximal size and then turn into contraction stage.     

Exact Boltzmann-Gas Filled Bianchi Type V Space-Times

Bianchi type V cosmological models are studied that contain a relativistic ideal Boltzmann gas. The effect of a cosmological constant upon the space-time geometry is also considered. In both high and low temperature limit the general solution of the Einstein gravitational field equations can be expressed in an exact closed parametric form. At final stages, depending on the presence or absence of the cosmological constant, cosmologies are driven to an isotropic inflationary open de Sitter type Universe or to an isotropic open Friedmann era.     

Hawking’s radiation in non-stationary rotating de Sitter background

Hawking’s radiation effect of Klein-Gordon scalar field, Dirac particles and Maxwell’s electromagnetic field in the non-stationary rotating de Sitter cosmological space-time is investigated by using a method of generalized tortoise co-ordinates transformation. The locations and the temperatures of the cosmological horizons of the non-stationary rotating de Sitter model are derived. It is found that the locations and the temperatures of the rotating cosmological model depend not only on the time but also on the angle. The stress-energy regularization techniques are applied to the two dimensional analog of the de Sitter metrics and the calculated stress-energy tensor contains the thermal radiation effect.     

Exact Nonbarotropic Bianchi Type I Universe

Bianchi type I cosmological models are studied that contain a nonbarotropic relativistic Boltzmann gas. The effect of a cosmological constant is considered too. In the limit of small temperatures the general solution of the Einstein gravitational field equations can be expressed in an exact closed parametrical form. At final stages, depending on the presence or absence of the cosmological constant, cosmologies are driven to an isotropic inflationary de Sitter Universe or to an isotropic Friedmann era. This revised version was published online in July 2006 with corrections to the Cover Date.     

A finite temperature λφ4 model and A De Sitter — Friedmann transition in the early universe

We have analysed the finite temperature λφ⁴ model in the Robertson Walker metric, taking into consideration spontaneous symmetry breaking, particle production and symmetry recovery through phase transition under a high temperature, and found that it is possible to have a cosmological model free of singularities. Such a model begins in the singularity-free, horizon-free, Beltrami-Anti-de Sitter state. Continual production of particles keeps on raising its temperature until a critical temperature T_C is reached, when a phase change takes place, and the universe is transformed into a radiation-dominated, thermally-expanding Friedmann state. This phase transition corresponds to a big-bang without, however, an antecedent singularity.     

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.