Cosmological principle and primordial spinor fields

An exact solution of Dirac's equation in an open Robertson-Walker universe is constructed such that the corresponding energy-momentum densityT _µv obeys the cosmological principle. However, in anopen universe, this principlemust always be violated by the other physical densities of the cosmological solution (e.g. pseudoscalar, (axial-) current and polarization). If the current densityj _µ = isrequired to obey the cosmological principle, then the universe must beflat.     

Cosmological dissipative structure

The concept of black hole entropy is generalized to cosmological event horizons. An analogue of the Bekenstein-Hawking generalized second law of thermodynamics is suggested. This law is illustrated by considering entropy changes in various black hole de Sitter spacetimes, and also with the help of a viscous-driven de Sitter universe model, which provides a cosmological version of a far-fromequilibrium dissipative structure. The law apparently fails for some recontractinguniverse models. This indicates that a contribution to the gravitational entropy has been omitted. A possible remedy involving algorithmic complexity theory is suggested. I propose the use of a cosmic entropy censorship hypothesis as a filter for acceptable field theories.     

Constraints on dark energy and modified gravity models by the Cosmological Redshift Drift test

We study cosmological constraints on the various accelerating models of the universe using the time evolution of the cosmological redshift of distant sources. The important characteristic of this test is that it directly probes the expansion history of the universe. In this work we analyze the various models of the universe which can explain the late time acceleration, within the framework of General Theory of Relativity (GR) (XCDM, scalar field potentials) and beyond GR (f(R)$f(R)$ gravity model).     

Aspects of Cosmological Relativity

In this paper we review cosmological relativity,a new special theory of relativity that was recentlydeveloped for cosmology, and discuss in detail some ofits aspects. We recall that in this theory it is assumed that gravitation is negligible.Under this assumption, the receding velocities ofgalaxies and the distances between them in the Hubbleexpansion are united into a four-dimensionalpseudo-Euclidean manifold, similarly to space and time inordinary special relativity. The Hubble law is assumedand is written in an invariant way that enables one toderive a four-dimensional transformation which issimilar to the Lorentz transformation. The parameter inthe new transformation is the ratio between the cosmictime to the Hubble time (in which the cosmic time ismeasured backward with respect to the present time). Accordingly, the new transformationrelates physical quantities at different cosmic times inthe limit of weak or negligible gravitation. Thetransformation is then applied to the problem of the expansion of the universe at the very earlystage when gravity was negligible and thus thetransformation is applicable. We calculate the ratio ofthe volumes of the universe at two different timesT₁ and T₂ after the big bang. Under theassumptions that T₂ – T₁ 10^-32 sec and T₂ 1 sec,we find that V₂/V₁ =10^-16/T₁. For T₁ 10^-132 sec we obtainV₂/V₁ 10⁵⁰. Thisresult conforms with the standard inflationary universe theory, but now it isobtained without assuming that the universe is propelledby antigravity. New applications of the theory arepresented. This includes a new law for the decay of radioactive materials that was recentlydeveloped by Carmeli and Malin. The new law is amodification of the standard exponential formula whencosmic times are considered instead of the ordinarylocal times. We also show that there is no need to assumethe existence of galaxy dark matter; the Tully-Fisherlaw is derived from our theory. A significant extensionof the theory to cosmology that was recently made by Krori, Pathak, Das, and Purkayastha isgiven. In this way cosmological relativity becomes ageneral theory of relativity in seven dimensions ofcurved space-time-velocity. The solutions of the field equations in seven dimensions obtained by Kroriet al. are given and compared to those of the standardFriedmann-Robertson-Walker result. A completely newpicture of the expanding universe is thus obtained and compared to the FRW one.     

Letter: A Cosmological Constant Interpreted as the Field Energy of a Quaternionic Field

The expression of a time-dependent cosmological constant 1/t² is interpreted as the energy density of a special type of the quaternionic field which is coupled to its own field energy. The general solution of the corresponding field equations yields the field energy which contains an integration constant t ₀. If t ₀ > 0 then the cosmological constant exhibits no initial singularity at t = 0. In the early universe the black energy associated with can be made small enough for the structure forming of galaxies getting, however, its observational value at the present time.     

Cosmological models with constant deceleration parameter in Brans-Dicke theory

A detailed study of cosmological models with constant deceleration parameterq is undertaken in the framework of Brans-Dicke theory. These models are divided into two categories: (i) singular models with expansion driven by big-bang impulse, (ii) non-singlar models with expansion driven by creation of matter particles. Prigogine's hypothesis of creation of matter out of gravitational energy is analysed and extended to BD cosmology. To accommodate the creation of new particles, the universe is regarded as an open thermodynamical system and the energy conservation equation is modified with the incorporation of a creation pressure termp _c in the energy-momentum tensor . The exact solutions of the field equations of BD theory with are obtained using the power law relation=KR , which leads to models with constantq. The behaviour of the solutions is investigated for different range of values ofa. The role played by the BD scalar field and creation of matter particles in the expansion of the universe is investigated. It is found that one particular model with constantq has exponential expansion.     

Cosmological models

An LRS Bianchi type II cosmological model is built with a state equation that is a function of the cosmic timet. The ratiop/ is 1/3 whent 0 and is insignificant whent. Thus, the matter content behaves like radiation for smallt and like dust for larget.     

Cosmological Relativity: Determining the Universe by the Cosmological Redshift as Infinite and Curved

Using cosmological relativity theory, we derive the formula for the cosmological redshift written explicitly in terms of 1 – , where = /_c is the ratio of the average mass density to the critical closure density. Based on the present day data of observed redshifts, we conclude that < 1, which means the universe is infinite and curved, and expands forever.     

Quantization of closed mini-superspace models as bound states

The Wheeler-DeWitt equation is applied to closedk>0 Friedmann-Robertson-Walker metric with various combination of cosmological constant and matter (e.g., radiation or pressureless gas). It is shown that if the universe ends in the matter dominated era (e.g., radiation or pressureless gas) with zero cosmological constant, then the resulting Wheeler-DeWitt equation describes a bound state problem. As solutions of a nondegenerate bound state system, the eigen-wave functions are real (Hartle-Hawking). Furthermore, as a bound state problem, there exists a quantization condition that relates the curvature of the three space with the various energy densities of the universe. If we assume that our universe is closed, then the quantum number of our universe isN(Gk)^–110¹²². The largeness of this quantum number is naturally explained by an early inflationary phase which resulted in a flat universe we observe today. It is also shown that if there is a cosmological constant >0 in our universe that persists for all time, then the resulting Wheeler-DeWitt equation describes a non-bound state system, regardless of the magnitude of the cosmological constant. As a consequence, the wave functions are in general complex (Vilenkin).     

A Cosmological Model of Thermodynamic Open Universe

In this paper we have given a generalization of the earlier work by Prigogine et al. (Gen. Relativ. Gravit. 19:1, 1989; Gen. Relativ. Gravit. 21(8):767–776, 1989) who have constructed a phenomenological model of entropy production via particle creation in the very early universe generated out of the vacuum rather than from a singularity, by including radiation also as the energy source and tried to develop an alternative cosmological model in which particle creation prevents the big bang. We developed Radiation dominated model of the universe which shows a general tendency that (i) it originates from instability of vacuum rather than from a singularity. (ii) Up to a characteristic time t _c cosmological quantities like density, pressure, Hubble constant and expansion parameter vary rapidly with time. (iii) After the characteristic time these quantities settles down and the models are turned into de-Sitter type model with uniform matter, radiation, creation densities and Hubble’s constant H. The de-Sitter regime survives during a decay time t _d then connects continuously to a usual adiabatic matter radiation RW universe. The interesting thing in the paper is that we have related the phenomenological radiation dominated model to macroscopic model of quantum particle creation in the early universe giving rise to the present observed value of cosmic background radiation. It is also found that the dust filled model tallies exactly with that of the Prigogine’s one, which justifies that our model is generalized Prigogine’s model. Although the model originates from instability of vacuum rather than from a singularity, still there is a couple of unavoidable singularities in the model.     

A critical density cosmological model with varying gravitational and cosmological “constants”

A cosmological model in which the universe has its critical density and the gravitational and cosmological constantsG and are time-dependent is presented. The model may possibly solve the horizon and monopole problems. It predicts a perpetually expanding universe in whichG increases and decreases with time in a manner consistent with conservation of the energy-momentum tensor. The model also allows the calculation of various cosmological parameters.     

5D generalized inflationary cosmology

We consider a 5D Kaluza-Klein type cosmological model with the fifth coordinate being a generalization of the invariant historical time of the covariant theory of Horwitz and Piron. We distinguish between vacuum-, off-shell matter-, and on-shell matter-dominated eras as the solutions of the corresponding 5D gravitational field equations, and build an inflationary scenario according to which passage from the off-shell matter-dominated era to the on-shell one occurs, probably as a phase transition. We study the effect of this phase transition on the expansion rate in both cases of localO(4,1) andO(3,2) invariance of the extended (x ^µ,) manifold and show that it does not change in either case. The expansion of the model we consider is not adiabatic; the thermodynamic entropy is a growing function of cosmic time for the closed universe, and can be a growing function of historical time for the open and the flat universe. A complete solution of the 5D gravitational field equations is obtained for the on-shell matter-dominated universe. The open and the closed universe are shown to tend asymptotically to the standard 4D cosmological models, in contrast to the flat universe which does not have the corresponding limit. Finally, possible cosmological implications are briefly discussed.     

Anisotropic Dark Energy Bianchi Type-II Cosmological Models in Lyra Geometry

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological model has been discussed in general relativity in the presence of a hypothetical anisotropic dark energy fluid with constant deceleration parameter within the frame work of Lyra’s manifold with uniform and time varying displacement field vector. With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a dark energy cosmological model is obtained in this theory. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

Cosmological Horizons and Reconstruction of Quantum Field Theories

As a starting point, we state some relevant geometrical properties enjoyed by the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds. Those properties are generalised to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon common to all co-moving observers. This structure is later exploited in order to recast, in a cosmological background, some recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable hypotheses on M, encompassing both the cosmological de Sitter background and a large class of other FRW spacetimes, the algebra of observables for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables constructed on the cosmological horizon. There is exactly one pure quasifree state λ on which fulfills a suitable energy-positivity condition with respect to a generator related with the cosmological time displacements. Furthermore λ induces a preferred physically meaningful quantum state λ _M for the quantum theory in the bulk. If M admits a timelike Killing generator preserving , then the associated self-adjoint generator in the GNS representation of λ _M has positive spectrum (i.e., energy). Moreover λ _M turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of an expanding de Sitter spacetime, λ _M coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity of the Hadamard property for λ _M in more general spacetimes are presented. Dedicated to Professor Klaus Fredenhagen on the occasion of his 60th birthday.     

Dynamics of anisotropic power-law <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) cosmology

Modified theories of gravity have attracted much attention of the researchers in the recent years. In particular, the f(R) theory has been investigated extensively due to important f(R) gravity models in cosmological contexts. This paper is devoted to exploring an anisotropic universe in metric f(R) gravity. A locally rotationally symmetric Bianchi type I cosmological model is considered for this purpose. Exact solutions of modified field equations are obtained for a well-known f(R) gravity model. The energy conditions are also discussed for the model under consideration. The viability of the model is investigated via graphical analysis using the present-day values of cosmological parameters. The model satisfies null energy, weak energy, and dominant energy conditions for a particular range of the anisotropy parameter while the strong energy condition is violated, which shows that the anisotropic universe in f(R) gravity supports the crucial issue of accelerated expansion of the universe.     

Cosmological applications in Kaluzaben Klein theory

The field equations of Kaluza-Klein (KK) theory have been applied in the domain of cosmology. These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor's expansion of cosmological function, Λ(t), up to the first order of the time t. The cosmological parameters are calculated and some cosmological problems are discussed.     

Cosmological solutions for the coupled Einstein-Yang-Mills-Higgs equations

The coupled system of Einstein-Yang-Mills-Higgs equations is solved numerically for a Robertson-Walker symmetric universe. The open universe must be excluded because, for this situation, the coupled system is unable to produce energy-momentum densityT in agreement with the Robertson-Walker symmetry. For the closed universe, inflation solutions do occur if an early re-collapse is avoided by suitable choice of the initial conditions. The energy exchange between the minimally coupled Higgs and Yang-Mills subsystems is very small so that the inflating power of the Higgs field cannot be disturbed by the presence of the Yang-Mills field. After the inflation phase the influence of the Yang-Mills field is completely negligible (cosmic no-hair theorem).     

A Quantum Universe and the Solution to the Cosmological Problems

We have found that the hierarchial problems appearing in cosmology are a manifestation of the quantum nature of the universe. The universe is still described by the same formulae that once hold at Planck's time. The universe is found to be governed by the Machian equation, GM = Rc ², where M and R are mass and radius of the universe. A Planck's constant xsfor different cosmic scales is provided. The status of the universe at different stages is shown to be described in terms of the fundamental constants (c, , G, , H) only. The concept of maximal (minimal) acceleration, power, temperature, etc., is introduced and justified.     

Cosmological Dynamics of the Tachyon with an Inverse Power-Law Potential

We investigate tachyon dynamics with an inverse power-law potential V () ^–. We find global attractors of the dynamics leading to a dust behavior for > 2 and to an accellerating universe for 0 < 2. We study linear cosmological perturbations and we show that metric fluctuations are constant on large scales in both cases. In the presence of an additional perfect fluid, the tachyon with this potential behaves as dust or dark energy.     

Cosmological bootstrap

The extremely large value of the cosmological constant that is characteristic of particle physics and the inflation of the early universe are inherently interconnected. One can construct a superpotential that, after consideration for the leading effects due to supergravity, produces a flat potential of inflaton with a constant density of energy V = Λ⁴. The introduction of relatively small quantum loop corrections to the parameters of this superpotential naturally leads to a dynamical instability taking the form of an inflationary regime of relaxation of the cosmological constant. This pattern is phenomenologically consistent with observational data at Λ ∼ 10¹⁶ GeV.