Generalized Isothermal Universes

We present a simple nonstatic generalization of the isothermal universe. The cosmological fluid obeys a barotropic equation of state of the form p=. We employ a causal heat transport equation of the Maxwell–Cattaneo form to study the thermodynamical behavior of our model.     

Entropies of the various components of the universe

In this study, we investigate the entropies of photons, ideal gas-like dust (baryonic matter), and a special kind of dark energy in the context of cosmology. When these components expand freely with the universe, we calculate the entropy and specific entropy of each component from the perspective of statistics. Under specific assumptions and conditions, the entropies of these components can satisfy the second law of thermodynamics independently. Our calculations show that the specific entropy of matter cannot be a constant during the expansion of the universe, except for photons. When these components interact with the space-time background, particle production (annihilation) can occur. We study the influence of the interaction on the entropies of these components and obtain the conditions guaranteeing that the entropy of each component satisfies the second law of thermodynamics.     

Particle masses in the early universe: Matter and entropy productions

This article deals with the particle and entropy productions in the early universe, which is regarded as a thermodynamically open system in the sense of Prigogine, by incorporating the epoch dependence of elementary particle masses. The epoch dependence of particle masses for some of the Robertson-Walker (RW) universes appears as a consequence of previous considerations of the hadronic matter extension in the inner space-time regarded as anisotropic and Finslerian in character. The nature of the evolution of the early universe has been discussed in the framework of the modified thermodynamic energy conservation law and the new mass formula apart from the other Einstein equation. The trivial solution of these equations is the usual inflationary stage of the early universe, whereas the matter-dominated RW universe appears as the nontrivial solution. It is shown that at the transition epocht=10^–23 sec the creation phenomenon stops and the usual cosmology of the radiation era follows with Pascal's equation of state. This model can also account for the observed specific entropy per baryon of the present universe and the generation of the large value ofK ^–1, whereK=Gm _p ² /c,m _p being the mass of the proton.     

Full Causal Theory of Bulk Viscosity and Specific Entropy of the Universe

This article deals with the full Israel–Stewart causal theory of bulk viscosity as employed to the dissipative expansion of the early universe. It is shown that the nontruncated full theory can be cast in the form of a noncausal theory with an auxiliary condition which states that the square of dissipative contribution to the speed of sound varies with the particle number in a comoving volume. Also, a generalized temperature appears in a cosmological invariant which is shown to hold good for the dissipative expansion in an intermediate brief transition period (around the epoch time = 10^–23 s) between the very early mild inflation stage of the universe and the standard radiation-dominated FRW era of it. With this generalized temperature, the Gibbs equation has been generalized. This equation is also shown to have an alternative form with a term depending on bulk viscosity. In the dissipative transition period, the universe as a thermodynamically open system of viscous fluid can generate specific entropy. In this period the temperature rose to a considerable extent. Due to the cosmological invariant, the dissipative contribution to the speed of sound and consequently the particle number decreased sharply, ensuring the second law of thermodynamics. It is possible to have an estimate of the specific entropy in consistency with the observations. The total entropy and the particle number of the observable universe have also been found here. These estimates agree with the accepted values for them.     

Mild Inflation and Modified General Relativity in the Early Universe

This article deals with particle creation andthe production of specific entropy per baryon in theearly universe, which is regarded as a thermodynamicallyopen system in the sense of Prigogine. The modified general relativity (MGR) theory of Rastall,Al-Rawaf, and Taha is employed. It contains an extraindependent constant which is peculiar to thenon-Newtonian regime, besides the usual gravitationalconstant. Usual general relativity (GR) appears here asa special case for = 1. With a modifiedthermodynamic energy conservation law, it is possible toobtain an equation for the expansion scalar byincorporating the epoch dependence of elementary particlemasses. The epoch dependence of particle masses for theRobertson-Walker (RW) universe appears as a consequenceof hadronic matter extension in a microlocal space-time regarded as anisotropic and Finslerian. Thegoverning equations in the present formalism specify theequation of state and give a solution for the expansionscalar. This solution represents a mild inflationary phase in the very early universe. It is alsoshown that there are no 'turn-on' and'turn-off' problems for this mild inflation.It can account for particle creation and production ofspecific entropy per baryon consistent with the observation. Theproduction of specific entropy per baryon is alsoconsidered here in the MGR framework with theintroduction of viscous pressure; the calculated valueis in good agreement with observation for the GR case, butfor the MGR case, in order to have its value withinobservational limits, must lie in the range 0.75 1. It is also argued that this formalismdoes not have horizon and flatnessproblems.     

Higher Dimensional Cosmological Model With Gravitational and Cosmological "Constants"

In this paper we have considered a cosmological model representing a flat viscous universe with variable G and in the context of higher dimensional spacetime. It has been observed that in this model the particle horizon exists and the cosmological term varies as inverse square of time. The deceleration parameter and temperature are well within the observational limits. The model indicates matter and entropy generation in the early stages of the universe. Further, it is shown that our model generates all models obtained by Arbab and Singh et al. in four-dimensional space-time.     

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.     

Accelerating Flat Universe and Analytic Study of the m-z Relation

An accelerating flat universe with a variable cosmological term is obtained in the Robertson-Walker metric. The variable cosmological term is defined by the correction terms of the metric tensor field. Simple solutions of the scale factor and the cosmological term are shown. In this model of the universe, the magnitude-redshift relation is analytically studied to see if the model reproduces the tendency of the present observational data. The equation of state parameter is touched.     

Primary Matter Creation in a Weyl–Dirac Cosmological Model

In the framework of an integrable Weyl–Dirac (W–D) theory a cosmological model is proposed. It describes a universe that began its expansion from a primary pre-Planckian geometric entity containing no matter. During the pre-Planckian period, from R ₀ =5.58×10 ^–36 cm to R_I=5.58×10 ^–34 cm, this embryonic universe has undergone a very rapid expansion and cosmic matter was created by geometry. At R_I the universe was already filled with matter having the Planckian density _P and being in the state of prematter (P=–), while the Weylian geometric elements were insignificant. This state is the Planckian egg that has served as the initial state of the singularity-free cosmological model ⁽¹⁾ considered in the framework of Einstein's general theory of relativity. The W–D character of the geometry and the cosmological constant are significant in the pre-Planckian period during the matter creation. In the dust-dominated period a relic of the W–D geometry causes a global dark matter effect. In between the pre-Planckian and dust period one has Einstein's framework and is negligible.     

Nonsingular cosmological model with matter creation and entropy production

The study of nonsingular cosmological models [4] based on a theory of gravitation in flat space-times [1] is continued. For a radiation free universe the solution of the model is given analytically. Under the assumption that entropy cannot decrease the cosmological constant must be zero. At the beginning of the universe all energy is in the form of gravitation. The universe contracts. Matter and radiation are created out of gravitational energy and entropy is produced. The contraction stops and then the universe expands without limit. The creation of matter continues producing entropy but today the production of matter and entropy is negligible. The density parameter ₀ 1, i.e. there must be missing mass in the universe. The flatness and the homogeneity problem are solved.     

Thermodynamics of diffusive DM/DE systems

We discuss the energy density, temperature and entropy of dark matter (DM) and dark energy (DE) as functions of the scale factor a in an expanding universe. In a model of non-interacting dark components we repeat a derivation from thermodynamics of the well-known relations between the energy density, entropy and temperature. In particular, the entropy is constant as a consequence of the energy conservation. We consider a model of a DM/DE interaction where the DM energy density increase is proportional to the particle density. In such a model the dependence of the energy density and the temperature on the scale factor a is substantially modified. We discuss (as a realization of the model) DM which consists of relativistic particles diffusing in an environment of DE. The energy gained by the dark matter comes from a cosmological fluid with a negative pressure. We define the entropy and free energy of such a non-equilibrium system. We show that during the universe evolution the entropy of DM is increasing whereas the entropy of DE is decreasing. The total entropy can increase (in spite of the energy conservation) as the DM and DE temperatures are different. We discuss non-equilibrium thermodynamics on the basis of the notion of the relative entropy.     

Thermodynamics and general relativity could determine the geometry of the universe

We introduce a suggestive model where certain quantities in Friedmann models are treated like their thermodynamic counterparts; temperature entropy, Gibbs energy, and so on. Within this model, changes in the symmetry of the universe are interpreted as first- or second-order phase transitions. The thermodynamics we introduce give us a new way of determining the geometry of the universe. By choosing a specific local equation of state (P=), we show that with respect to the thermodynamics we have introduced, it is always more advantageous for the universe to be in a Bianchi V (open) symmetric state.This essay received an honorable mention from the Gravity Research Foundation for the year 1986 — Ed.     

THE ORIGIN OF ENTROPY IN THE UNIVERSE

We discuss the entropy generation in quantum tunneling of a relativistic particle under the influence of a time-varying force with the help of squeezing formalism. It is shown that if one associates classical coarse grained entropy to the phase space volume, there is an inevitable entropy growth due to the changes in position and momentum variances. The entropy change can be quantified by a simple expression S=ln cosh 2r, where r, is the squeeze parameter measuring the height and width of the potential barrier. We suggest that the universe could have acquired its initial entropy in a quantum squeeze from nothing and briefly discuss the implications of our proposal.     

The Global Arrow of Time as a Geometrical Property of the Universe

Traditional discussions about the arrow of time in general involve the concept of entropy. In the cosmological context, the direction past-to-future is usually related to the direction of the gradient of the entropy function of the universe. But the definition of the entropy of the universe is a very controversial matter. Moreover, thermodynamics is a phenomenological theory. Geometrical properties of space-time provide a more fundamental and less controversial way of defining an arrow of time for the universe as a whole. We will call the arrow defined only on the basis of the geometrical properties of space-time, independently of any entropic considerations, the global arrow of time. In this paper we will argue that: (i) if certain conditions are satisfied, it is possible to define a global arrow of time for the universe as a whole, and (ii) the standard models of contemporary cosmology satisfy these conditions.     

Thermodynamics of gravitationally induced particle creation scenario in DGP braneworld

In this paper, we discuss the thermodynamical analysis for gravitationally induced particle creation scenario in the framework of DGP braneworld model. For this purpose, we consider apparent horizon as the boundary of the universe. We take three types of entropy such as Bakenstein entropy, logarithmic corrected entropy and power law corrected entropy with ordinary creation rate \(\Gamma \). We analyze the first law and generalized second law of thermodynamics analytically for these entropies which hold under some constraints. The behavior of total entropy in each case is also discussed which implies the validity of generalized second law of thermodynamics. Also, we check the thermodynamical equilibrium condition for two phases of creation rate, that is constant and variable \(\Gamma \) and found its vitality in all cases of entropy.     

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.     

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.