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.     

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).     

Stress-energy connection and cosmological constant problem

We study gravitational properties of vacuum energy by erecting a geometry on the stress-energy tensor of vacuum, matter and radiation. Postulating that the gravitational effects of matter and radiation can be formulated by an appropriate modification of the spacetime connection, we obtain varied geometrodynamical equations which properly comprise the usual gravitational field equations with, however, Planck-suppressed, non-local, higher-dimensional additional terms. The prime novelty brought about by the formalism is that, the vacuum energy does act not as the cosmological constant but as the source of the gravitational constant. The formalism thus deafens the cosmological constant problem by channeling vacuum energy to gravitational constant. Nevertheless, quantum gravitational effects, if any, restore the problem via the graviton and graviton-matter loops, and the mechanism proposed here falls short of taming such contributions to cosmological constant.     

Inflationary Cosmology with Scalar Field and Radiation

We present a simple, exact and self-consistentcosmology with a phenomenological model of quantumcreation of radiation due to decay of the scalar field.The decay drives a non-isentropic inflationary epoch, which exits smoothly to the radiation era,without reheating. The initial vacuum for radiation isa regular Minkowski vacuum. The created radiation obeysstandard thermodynamic laws, and the total entropyproduced is consistent with the accepted value.We analyze the difference between the present model andthe model with the decaying cosmological constantconsidered in [1].     

Friedmann cosmology with decaying vacuum density

Among the several proposals to solve the incompatibility between the observed small value of the cosmological constant and the huge value obtained by quantum field theories, we can find the idea of a decaying vacuum energy density, leading from high values at early times of universe evolution to the small value observed nowadays. In this paper we consider a variation law for the vacuum density recently proposed by Schützhold on the basis of quantum field estimations in the curved, expanding background, characterized by a vacuum density proportional to the Hubble parameter. We show that, in the context of an isotropic and homogeneous, spatially flat model, the corresponding solutions retain the well established features of the standard cosmology, and, in addition, are in accordance with the observed cosmological parameters. Our scenario presents an initial phase dominated by radiation, followed by a dust era long enough to permit structure formation, and by an epoch dominated by the cosmological term, which tends asymptotically to a de Sitter universe. Taking the matter density equals to half of the vacuum energy density, as suggested by observation, we obtain a universe age given by Ht = 1.1, and a decelerating parameter equals to −1/2.     

Model of an early stage in the evolution of the universe

An open isotropic cosmological model is considered, with nonzero cosmological constant and consideration of spontaneous disruption of symmetry and vacuum polarization. It is shown that consideration of quantum effects leads to the absence of initial singularity and de Sitter expansion. The problem of the vacuum energy-momentum tensor corresponding to fields of a quantum nature is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 54–58, November, 1986.     

Quantum mechanical look at the radioactive-like decay of metastable dark energy

We derive the Shafieloo, Hazra, Sahni and Starobinsky (SHSS) phenomenological formula for the radioactive-like decay of metastable dark energy directly from the principles of quantum mechanics. To this aim we use the Fock–Krylov theory of quantum unstable states. We obtain deeper insight on the decay process as having three basic phases: the phase of radioactive decay, the next phase of damping oscillations, and finally the phase of power-law decay. We consider the cosmological model with matter and dark energy in the form of decaying metastable dark energy and study its dynamics in the framework of non-conservative cosmology with an interacting term determined by the running cosmological parameter. We study the cosmological implications of metastable dark energy and estimate the characteristic time of ending of the radioactive-like decay epoch to be \(2.2\times 10^4\) of the present age of the Universe. We also confront the model with astronomical data which show that the model is in good agreement with the observations. Our general conclusion is that we are living in the epoch of the radioactive-like decay of metastable dark energy which is a relict of the quantum age of the Universe.     

Inhomogeneous Cosmologies with Tachyonic Dust as Dark Matter

A cosmology is considered driven by a stress-energy tensor consisting of a perfect fluid, an inhomogeneous pressure term (which we call a tachyonic dust for reasons which will become apparent) and a cosmological constant. The inflationary, radiation dominated and matter dominated eras are investigated in detail. In all three eras, the tachyonic pressure decreases with increasing radius of the universe and is thus minimal in the matter dominated era. The gravitational effects of the dust, however, may still strongly affect the universe at present time. In case the tachyonic pressure is positive, it enhances the overall matter density and is a candidate for dark matter. In the case where the tachyonic pressure is negative, the recent acceleration of the universe can be understood without the need for a cosmological constant. The ordinary matter, however, has positive energy density at all times. In a later section, the extension to a variable cosmological term is investigated and a specific model is put forward such that recent acceleration and future re-collapse is possible.     

The graviton one-loop effective action in cosmological space-times with constant deceleration

We consider the quantum Friedmann equations which include one-loop vacuum fluctuations due to gravitons and scalar field matter in a FLRW background with constant . After several field redefinitions, to remove the mixing between the gravitational and matter degrees of freedom, we can construct the one-loop correction to the Friedmann equations. Due to cosmological particle creation, the propagators needed in such a calculation are typically infrared divergent. In this paper we construct the graviton and matter propagators, making use of the recent construction of the infrared finite scalar propagators calculated on a compact spatial manifold in Janssen et al. (2008) [1]. The resulting correction to the Friedman equations is suppressed with respect to the tree level contribution by a factor of and shows no secular growth.     

Physical implications of the cosmological constant

The contribution of the quantum vacuum to the energy-momentum stress tensor in Einstein's field equations is very large. The observed cosmos is not in agreement with such a large term; thus, we require the presence of a cosmological constant to cancel this term. We discuss why this constant cannot originate from a quantum field or the gravitational field. We propose that this constant is physical evidence of the structure of space. The physical structure of space gives space an existence independent of the existence of matter and radiation.     

Vacuum Energy as the Origin of the Gravitational Constant

We develop a geometro-dynamical approach to the cosmological constant problem (CCP) by invoking a geometry induced by the energy-momentum tensor of vacuum, matter and radiation. The construction, which utilizes the dual role of the metric tensor that it structures both the spacetime manifold and energy-momentum tensor of the vacuum, gives rise to a framework in which the vacuum energy induced by matter and radiation, instead of gravitating, facilitates the generation of the gravitational constant. The non-vacuum sources comprising matter and radiation gravitate normally. At the level of classical gravitation, the mechanism deadens the CCP yet quantum gravitational effects, if strong, can keep it existent.     

Relaxation of vacuum energy in <Emphasis Type="Italic">q</Emphasis>-theory

The q-theory formalism aims to describe the thermodynamics and dynamics of the deep quantum vacuum. The thermodynamics leads to an exact cancellation of the quantum-field zero-point-energies in equilibrium, which partly solves the main cosmological constant problem. But, with reversible dynamics, the spatially flat Friedmann–Robertson–Walker universe asymptotically approaches the Minkowski vacuum only if the Big Bang already started out in an initial equilibrium state. Here, we extend q-theory by introducing dissipation from irreversible processes. Neglecting the possible instability of a de-Sitter vacuum, we obtain different scenarios with either a de-Sitter asymptote or collapse to a final singularity. The Minkowski asymptote still requires fine-tuning of the initial conditions. This suggests that, within the q-theory approach, the decay of the de-Sitter vacuum is a necessary condition for the dynamical solution of the cosmological constant problem.     

Dynamical Vacuum in Quantum Cosmology

By regarding the vacuum as a perfect fluid with equation of state p = -, de Sitter's cosmological model is quantized. Our treatment differs from previous ones in that it endows the vacuum with dynamical degrees of freedom, following modern ideas that the cosmological term is a manifestation of the vacuum energy. Instead of being postulated from the start, the cosmological constant arises from the degrees of freedom of the vacuum regarded as a dynamical entity, and a time variable can be naturally introduced. Taking the scale factor as the sole degree of freedom of the gravitational field, stationary and wave-packet solutions to the Wheeler-DeWitt equation are found, whose properties are studied. It is found that states of the Universe with a definite value of the cosmological constant do not exist. For the wave packets investigated, quantum effects are noticeable only for small values of the scale factor, a classical regime being attained at asymptotically large times.     

Vacuum energy and the universe in special relativity

The problem of the cosmological constant and vacuum energy is usually thought of as the subject of general relativity. However, vacuum energy is important for the Universe even in the absence of gravity, i.e., in the case when Newton’s constant G is exactly zero, G=0. We discuss the response of the vacuum energy to the perturbations of the quantum vacuum in special relativity and find that, as in general relativity, the vacuum energy density is on the order of the energy density of matter. In general relativity, the dependence of the vacuum energy on the equation of state of matter does not contain G and thus is valid in the limit G→0. However, the result obtained for the vacuum energy in a world without gravity, i.e., when G=0 exactly, is different.     

Noether symmetry for Gauss–Bonnet dilatonic gravity

Noether symmetry for Gauss–Bonnet Dilatonic interaction exists for a constant dilatonic scalar potential and a linear functional dependence of the coupling parameter on the scalar field. The symmetry with the same form of the potential and coupling parameter exists all in the vacuum, radiation and matter dominated era. The late time acceleration is driven by the effective cosmological constant rather than the Gauss–Bonnet term, while the later compensates for the large value of the effective cosmological constant giving a plausible answer to the well-known coincidence problem.     

Variable-G cosmology and creation

It has recently been asserted that a universe with a time-varying gravitational constantG necessarily implies creation if the rest mass of matter particles is constant. It is shown that this is not necessarily true. An example of a cosmological model with variableG and is presented, in which there is no creation and in which the rest mass of matter particles is constant.     

Wormholes, Classical Limit and Dynamical Vacuum in Quantum Cosmology

First a Friedmann-Robertson-Walker (FRW)universe filled with dust and a conformally invariantscalar field is quantized. For the closed model we finda discrete set of wormhole quantum states. In the case of flat spacelike sections we find states withclassical behaviour at small values of the scale factorand quantum behaviour for large values of the scalefactor. Next we study a FRW model with a conformally invariant scalar field and a nonvanishingcosmological constant dynamically introduced byregarding the vacuum as a perfect fluid with equation ofstate p = –. The ensuing Wheeler-DeWittequation turns out to be a bona fide Schrodinger equation, andwe find that there are realizable states with a definitevalue of the cosmological constant. Once again we findfinite-norm solutions to the Wheeler-DeWitt equation with definite values of thecosmological constant that represent wormholes,suggesting that in quantum cosmological models with asimple matter content wormhole states are a commonoccurrence.     

Turbulent Perfect Fluid Analogy for an Inflationary Nonsingular Vacuum Bubble and the Strong Energy Condition Within a String Derived Cosmology

A simple, consistent inflationary cosmology is developed from the basic structure of the -model expansion in string theory, which corresponds to the low energy effective ( 0) limit. The classical dilaton background solution is subject to stochastic vacuum fluctuations near the Planck scale. The motivation here is that the coupling of stochastic noise to a classical field theory often provides workable and powerful methodologies with which to explore quantum behaviour, turbulence and pattern and structure formation. The dilaton fluctuations induce random (Weyl) conformal fluctuations in the Einstein frame metric. The additional vacuum stress-energy tensor—which the fluctuations induce within the string derived Einstein-dilaton field equations—can be interpreted and described in terms of a "turbulent perfect fluid" with a fluctuating negative pressure. A (stochastic) de-Sitter solution describes a turbulent, inflating vacuum bubble whose exponential expansion is future-eternal and unbounded; but the vacuum turbulence breaks the spherical symmetry and homogeneity usually associated with a smooth de-Sitter solution. Consequently, the strong energy condition (SEC) is violated for the turbulent perfect fluid tensor describing the (false) vacuum—this suggests that there is no initial singularity. With a suitable "rollover" dilaton potential V() there can then be a phase transition to a hot Friedmann expanding universe at the minima of the potential as _o. Assuming an instantaneous decay of the inflaton to a perfect fluid of thermal radiation, the de-Sitter and Friedman solutions are matched using a step function. However, the residual vacuum turbulence carried over from inflation, breaks the usual homogeneity and symmetry of the FRW solutions. The induced cosmological constant plays a role somewhat like a Reynold's number for a non-linear, turbulent fluid. The SEC—and therefore the Hawking singularity theorem—is obeyed only after inflation, so it appears that the universe is singular only within the perspective of a matter or radiation fluid dominated era; but past directed matter worldlines do not converge in the past since they cannot be extrapolated beyond the (phase) transition at which the turbulent vacuum bubble decayed. On cosmic time scales, the vacuum "turbulence" augments both cosmic acceleration (the Hubble parameter) and distances with respect to the standard, classical Friedman RW cosmologies.     

Evolution of the cosmological constant in effective gravity

In contrast to the phenomenon of nullification of the cosmological constant in equilibrium vacuum, which is the general property of any quantum vacuum, there are many options in modifying the Einstein equation to allow the cosmological constant to evolve in a nonequilibrium vacuum. An attempt is made to extend the Einstein equation in the direction suggested by the condensed matter analogy of the quantum vacuum. Different scenarios are found depending on the behavior of and the relation between the relaxation parameters involved, some of these scenarios having been discussed in the literature. One of them reproduces the scenario in which the effective cosmological constant emerges as a constant of integration. The second one describes the situation when, after the cosmological phase transition, the cosmological constant drops from zero to a negative value; this scenario describes the relaxation from this big negative value back to zero and then to a small positive value. In the third example, the relaxation time is not a constant but depends on matter; this scenario demonstrates that vacuum energy (or its fraction) can play the role of cold dark matter.