The Very Early Universe might not have been Radiation-Dominated

The equation of state of the very early Universe and the formula for the radius, are here evaluated. It is shown that the very early classical Universe might not be radiation-dominated, although we do not exclude the existence of the radiation dominated phase for the early, but not the very early Universe. This revised version was published online in July 2006 with corrections to the Cover Date.     

The possible compatibility of Einstein's general theory of relativity,Mach's principle,and Rosen's bimetric theory,in relation to Horák's cosmic potential

Mach's principle is formulated in two different ways, heuristic and mathematical. Known problems of the principle are listed and two of them, the problem of its validity in the case the Universe is open and the boundary condition problem, are analyzed separately. Moreover, the history of the cosmic potential is outlined and a short modification of Horák's deduction of the potential is presented together with a discussion on the conditions of the solution. The conclusions are drawn that the Universe is closed and that Mach's principle is compatible with the general theory of relativity, provided that the Big Bang did not start from a singularity but from finite volume and density. In the last section it is shown that Rosen's bimetric theory is compatible with our picture of the Universe.     

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.     

Exact solutions: classical electron model

Rahaman et al. (Astrophys. Space. Sci. 331:191–197, 2010) discussed some classical electron models (CEM) in general relativity. Bijalwan (Astrophys. Space. Sci. 334:139–143, 2011) present a general exact solution of the Einstein-Maxwell equations in terms of pressure. We showed that charged fluid solutions in terms of pressure are not reducible to a well behaved neutral counter part for a spatial component of metrice ^λ . Hence, these solutions represent an electron model in general relativity. We illustrated solutions in terms of pressure briefly with de-Sitter equation of state and charged analogues of Kohler Chao interior solution as a special cases.     

Clustering of non-point mass system of galaxies in the expanding Universe

We derive the cosmic energy equation for the non-point mass system of galaxies (galaxies with halos) by using the adiabatic approximation for the growth of gravitational clustering of galaxies in the expanding Universe. The cosmic energy equation so derived represents the general form of conservation of energy for the expanding volume. Using the derived form of cosmic energy equation we try to study the evolution of correlation potential energy of the system. We also try to explore the condition under which the approximation of extensivity may be applied to the infinite gravitating non-point mass system of galaxies.     

Distance measurements as a probe of cosmic acceleration

A major recent development in observational cosmology has been an accurate measurement of the luminosity distance–redshift relation out to redshifts z =0.8 from Type Ia supernova standard candles. The results have been argued as evidence for cosmic acceleration. It is well known that this assertion depends on the assumption that we know the equation of state for all mass–energy other than normal pressureless matter; popular models are based either on the cosmological constant or on the more general quintessence formulation. However, this assertion also depends on a number of other assumptions, implicit in the derivation of the standard cosmological field equations: large-scale isotropy and homogeneity, the flatness of the Universe, and the validity of general relativity on cosmological scales (where it has not been tested). A detailed examination of the effects of these assumptions on the interplay between the luminosity distance–redshift relation and the acceleration of the Universe is not possible unless one can define the precise nature of the failure of any particular assumption. However a simple quantitative investigation is possible and reveals a number of considerations about the relative importance of the different assumptions. In this paper we present such an investigation. We find that the relationship between the distant-redshift relation and the sign of the deceleration parameter is fairly robust and is unaffected if only one of the assumptions that we investigate is invalid so long as the deceleration parameter is not close to zero (it would not be close to zero in the currently favoured Ω_Λ=1−Ω_matter=0.7 or 0.8 Universe, for example). Failures of two or more assumptions in concordance may have stronger effects.     

Cosmic acceleration and extra dimensions: constraints on modifications of the Friedmann equation

An alternative to dark energy as an explanation for the present phase of accelerated expansion of the Universe is that the Friedmann equation is modified, e.g. by extra dimensional gravity, on large scales. We explore a natural parametrization of a general modified Friedmann equation, and find that the present supernova Type Ia and cosmic microwave background data prefer a correction of the form 1/ H to the Friedmann equation over a cosmological constant.     

Can Lyra geometry explain the singularity free as well as accelerating Universe?

Observations of high red shift supernovae indicate that the Universe is accelerating. Existence of Big-bang singularity is one of the basic failures of general theory of relativity. In this letter we show that within the framework of Lyra geometry, the space-time of the Universe is not only free of Big-bang singularity but also exhibits acceleration during its evolution.     

Exact solutions of a flat cosmological model in BSTT

We solve the cosmological equations for the bimetric scalar—tensor theory of gravitation (BSTT) for a flat model of the Friedmann type with the equation of state p = a. In the initial stage of expansion, the energy density of the scalar field dominates over the energy density of matter. As a result, the behavior of the solution in this limit does not depend on a. For later stages of expansion of the Universe, the solution obtained goes to a special solution having the form of a power law function of time. In this case, the relative change in the gravitational scalar is proportional to the Hubble parameter. In the limit of large values for the parameter of the theory, only a simple solution with zero value of the constant of integration goes to the corresponding Friedmann solution of general relativity theory.Translated from Astrofizika, Vol. 37, No. 2, pp. 351–362, April–June, 1994.I would like to thank L. Sh. Grigoryan for valuable discussions and support.     

Does multiclustering of galaxy aggregates appear as a specific coil of extragalactic data unseparated from interpretations of the role of interstellar obscuration?

The use of a cosmic potential in relativistic cosmology is criticized. It is pointed out that the energetic closure of the Universe follows from general relativity and from quantized superspace cosmology without the introduction of the cosmic potential.     

Virialization of cosmological structures in models with time-varying equation of state

We study the virialization of the cosmic structures in the framework of flat cosmological models where the dark energy component plays an important role in the global dynamics of the Universe. In particular, our analysis focuses on the study of the spherical matter perturbations, as the latter decouple from the background expansion, start to 'turn around' and finally collapse. We generalize this procedure, taking into account models with an equation of state which vary with time, and provide a complete formulation of the cluster virialization attempting to address the non-linear regime of structure formation. In particular, assuming that clusters have collapsed prior to the epoch of z _f≃ 1.4, in which the most distant cluster has been found, we show that the behaviour of the spherical collapse model depends on the functional form of the equation of state.     

General relativistic singularity-free cosmological model

We “explain”, using a Classical approach, how the Universe was created out of “nothing”, i.e., with no input of initial energy nor mass. The inflationary phase, with exponential expansion, is accounted for, automatically, by our equation of state for the very early Universe. This is a Universe with no-initial infinite singularity of energy density.     

On spin-driven inflation from inflation fields in General Relativity and COBE data

Obukhov spin-driven inflation in general relativity is extended to include inflation fields. A de Sitter phase solution is obtained and new slow-rolling conditions for the spin potential are obtained. The spin potential reduces to Obukhov result at the present epoch of the Universe where the spin density is low with comparison to the Early Universe spin densities. A relation between the spin density energy and the temperature fluctuation can be obtained which allow us to determine the spin density energy in terms of the COBE data for temperature fluctuations.     

Cosmic equation of state and advanced LIGO-type gravitational wave experiments

It is hoped that the future generation of interferometric gravitational wave detectors will provide accurate measurements of the final stages of binary in-spirals. The sources probed by such experiments are of extragalactic origin and the observed chirp mass is the intrinsic chirp mass multiplied by (1+ z ) where z is the redshift of the source. Moreover the luminosity distance is a direct observable in such experiments. This creates the possibility to establish a new kind of cosmological test, supplementary to more standard ones.
Recent observations of distant type Ia supernovae light curves suggest that the expansion of the Universe has recently begun to accelerate. A popular explanation of the present accelerating expansion of the Universe is to assume that some part Ω_Q of the matter–energy density is in the form of a dark component called 'the quintessence' with the equation of state p _Q= wρ _Q with w ≥−1 . In this paper we consider the predictions concerning observations of binary in-spirals in future LIGO-type interferometric experiments assuming a 'quintessence cosmology'. In particular we compute the expected redshift distributions of observed events in the a priori admissible range of parameters describing the equation of state for the quintessence. We find that this distribution has a robust dependence on the cosmic equation of state.     

WD 1953−011: a magnetic white dwarf with peculiar field structure

We present a new interpretation of recent observations suggesting that the expansion of the Universe has recently started to accelerate. A cosmological model with a quintessence field driven by a potential motivated by M-theory is used to study the energy density and equation of state for the Universe. We find that late-time acceleration does not have to lead to the usual predictions of perpetual acceleration. The model allows another broad class of scenarios in which today's acceleration is a transient phenomenon, which is succeeded by a return to matter domination and decelerating expansion.     

Anisotropic fluid distributions in bimetric general relativity

Static and spherically-symmetric solutions of the field equations in the bimetric theory of gravitation are obtained for isotropic and anisotropic distributions of matter when the physical metric admits a one-parameter group of conformal motions. The solutions agree with Einstein's general relativity for physical systems comparable to the size of the Universe, such as the solar system.     

The Friedmann universe and the world potential

In Section 1 of the paper the energy equation of the Friedmann universe, when matter dominates over radiation, is discussed. It is known that the value of the world potential is constant everywhere in the Universe, despite the pulsation motion of the Universe or a possible transformation of pulsation energy into matter or vice versa. The condition for the Universe being closed is deduced. Furthermore, the possibility to define the mass-energy of the Universe is discussed; and the conclusion is arrived at that the mass-energy of the Universe relative to an observer in the non-metric space outside the Universe is equal to zero; i.e. the Universe originated as a vacuum fluctuation. Finally, the view-point of an external observer is described. Such an observer can claim that our closed Universe is a black hole in a non-metric empty space. Besides, the differences between such a black hole and the astrophysical black holes are indicated.In Section 2 the origin of the gravitational force retarding the expansion is discussed, using the properties of the relativistic gravitational potential. In contradiction to Section 1, the view-point of an inner observer (inside the Universe) is used here. It is concluded that the boundary of the closed Universe is an unlocalizable potential barrier.In Section 3 of the paper the apparent discrepancy between Mach's principle and the general theory of relativity is resolved. The solution is based on the fact that, for the Euclidean open universe, the concept of mass is related to the potential of the background equal to –1, but the concept of the mass-energy is related to the zero-potential of the non-metric background. Because the universe is open and a potential barrier (a boundary of the universe) can be localized-i.e. is geometrically existing — by solution of the field equation, we have to refer to the background with zero-potential. The principal idea of the solution is then that the zero-density means the density of mass-energy, when simultaneously the mass density is equal to the critical value for which the Robertson-Walker metric becomes the Euclidean metric of the Minkowski (i.e., flat) space-time. Further a generalization of Newton's law of inertia is formulated, and the properties of nullgeodesics are touched upon. As a conclusion it is stated that this paper and the two previous ones (see Voráek, 1979a, b)de facto express Mach's principle.     

The comparative analysis of dense stellar models governed by quadratic and linear equations of state

In the present article we construct physically viable models of anisotropic charged compact stellar objects admitting quadratic equation of state and linear equation of state. We analyze the physical behavior of compact star models 4U1538-52, LMCX-4, and Vela X-1 with in the frame work of general relativity. Our stellar models are free from singularities, satisfy all energy conditions and exhibit physically admissible characters. The necessary stability criteria viz. Buchdhal condition, adiabatic index and causality condition all stand true for our charged anisotropic compact stellar models. We also inspect the physical characteristics of compact stars via Linear equation of state by applying slight changes in the parameters of the models pertaining to Quadratic equation of state and analyze the models in the perspective of both equations of state. We study the physical attributes of the model 4U1538-52 extensively by implementing analytical and graphical tools. The models retain their validity for both linear as well as quadratic equations of state, however there is a slight variation in few attributes of the models.     

Nucleosynthesis in bouncing cosmologies

It is shown that certain anomalies connected with the primordial abundances of light nuclei may be resolved if it is assumed that the Universe oscillates between phases of finite densities. Since general relativity does not produce bouncing models of the Universe, such models are obtained through the introduction of a negative energy scalar field of zero rest mass. It is shown that all the relevant parameters of the dynamics of the model and the nucleosynthesis in it are determined by observations and that a self-consistent picture emerges. The model is capable of admitting more than three neutrino flavours without an embarrassingly high primordial helium content. It is also shown that the calculations could be adapted to described production of light nuclei in compact massive bouncing objects.     

An investigation of gravitational lens determinations of H0 in quintessence cosmologies

There is growing evidence that the majority of the energy density of the Universe is not baryonic or dark matter, but rather it resides in an exotic component with negative pressure. The nature of this 'quintessence' influences our view of the Universe, modifying angular diameter and luminosity distances. Here, we examine the influence of a quintessence component upon gravitational lens time-delays. As well as a static quintessence component, an evolving equation of state is also considered. It is found that the equation of state of the quintessence component and its evolution influence the value of the Hubble constant derived from gravitational lenses. However, the differences between evolving and non-evolving cosmologies are relatively small. We undertake a suite of Monte Carlo simulations to examine the potential constraints that can be placed on the universal equation of state from the monitoring of gravitational lens systems, and demonstrate that at least an order of magnitude more lenses than currently known will have to be discovered and analysed to accurately probe any quintessence component.