The vanishing likelihood of space-time singularity in quantum conformal cosmology

A general formalism is developed for studying the behavior of quantized conformal fluctuations near the space-time singularity of classical relativistic cosmology. It is shown that if the material contents of space-time are made of massive particles which obey the principle of asymptotic freedom and interact only gravitationally, then it is possible to estimate the quantum mechanical probability that, of the various possible conformal transforms of the classical Einstein solution, the actual model had a singularity in the past. This probability turns out to be vanishingly small, thus indicating that within the regime of quantum conformal cosmology it is extremely unlikely that the universe originated out of a space-time singularity.     

Tomographic entropy and cosmology

The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free pointlike particle and repulsive oscillator are considered. The notion of tomographic entropy and its properties are used to find some inequalities for the tomographic probability determining the quantum state of the universe. The sense of the inequality as a lower bound for the entropy is clarified.     

Consistent Histories in Quantum Cosmology

We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmological model sourced with a free massless scalar field, we calculate the probability that the universe is singular in the sense that it assumes zero volume. Classical solutions of this model are a disjoint set of expanding and contracting singular branches. A naive assessment of the behavior of quantum states which are superpositions of expanding and contracting universes suggests that a “quantum bounce” is possible i.e. that the wave function of the universe may remain peaked on a non-singular classical solution throughout its history. However, a more careful consistent histories analysis shows that for arbitrary states in the physical Hilbert space the probability of this Wheeler-DeWitt quantum universe encountering the big bang/crunch singularity is equal to unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a “quantum bounce” is thus not possible in these models.     

Is the cosmological singularity thermodynamically possible?

The four broad approaches that have been suggested heretofore to eliminate the initial singularity from cosmology are briefly reviewed. None is satisfactory, basically because one does not know enough about the microphysics involved in the process. Thermodynamics has often been used in such dilemmas, and it is proposed to answer the question of whether there was a Friedmann-like singularity in the universe by exploiting the bound on specific entropy that has been established for finite system. It is made applicable to the universe by considering only a causally connected spacelike region within the particle horizon of a given observer. It is found that the specific entropy of radiation in such a region can exceed the bound if the observer is too early in the universe. Faith in the bound leads to the conclusion that the Friedmann models cannot be extrapolated back to nearer than a few Planck-Wheeler times from the singularity. The Friedmann initial singularity thus appears to be thermodynamically unacceptable.     

A Non-Singular Universe with Vacuum Energy

A model for the universe based on the back-reaction effects of quantum fields at finite temperature in the background of Robertson-Walker spacetime and in the presence of a non-zero cosmological constant is constructed. We discuss the vacuum regime in the light of the results obtained through previous studies of the back-reaction of massless quantum fields in the static Einstein universe, and we argue that an adiabatic vacuum state and thermal equilibrium is achieved throughout this regime. Critical density is maintained naturally from the very early stages as a consequence of back-reaction effect of the vacuum fluctuations of quantum fields. Results show that such a model can explain many features of the early universe as well as the present universe. The model is free from the basic problems of the standard Friedmann cosmology, and is non-singular but involves a continuous creation of energy at a rate proportional to the size of the universe, which is lower than that suggested by the steady-state cosmology.     

Properties of the quantum universe in quasistationary states and cosmological puzzles

Old and new puzzles of cosmology are reexamined from the point of view of the quantum theory of the universe developed here. It is shown that in the proposed approach the difficulties of the standard cosmology do not arise. The theory predicts the observed dimensions of the non-homogeneities of matter density and the amplitude of fluctuations of the cosmic background radiation temperature in the Universe and points to a new quantum mechanism of their origin. The large-scale structure in the Universe is explained by the growth of non-homogeneities which arise from primordial quantum fluctuations due to the finite width of the quasistationary states. The theory allows one to obtain the value of the deceleration parameter, which is in good agreement with the recent SNe Ia measurements. It explains the large value of the entropy of the Universe and describes other parameters. Received: 30 July 2001 / Published online: 8 February 2002     

Dressing up a Reissner naked singularity

Spontaneous pair creation in the field of a large Reissner singularity (a point-like charge e whose mass M is such that $\text{MG}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{< e}$) is here considered. Using as a guide the definition of the positive and negative energy states of a classical particle in this field, a particular basis of quantum states is chosen which contains resonance states — these are interpreted by invoking particle creation. Extremely energetic particles are shown to burst out to infinity whereas the antiparticles dress up and neutralize the singularity. This result is contrasted with the process of pair production by black holes and compared with the isotropization of the early universe by creation of matter.     

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.     

Confronting dark energy models mimicking ΛCDM epoch with observational constraints: Future cosmological perturbations decay or future Rip?

We confront dark energy models which are currently similar to ΛCDM theory with observational data which include the SNe data, matter density perturbations and baryon acoustic oscillations data. DE cosmology under consideration may evolve to Big Rip, type II or type III future singularity, or to Little Rip or Pseudo-Rip universe. It is shown that matter perturbations data define more precisely the possible deviation from ΛCDM model than consideration of SNe data only. The combined data analysis proves that DE models under consideration are as consistent as ΛCDM model. We demonstrate that growth of matter density perturbations may occur at sufficiently small background density but still before the possible disintegration of bound objects (like clusters of galaxies, galaxies, etc.) in Big Rip, type III singularity, Little Rip or Pseudo-Rip universe. This new effect may bring the future universe to chaotic state well before disintegration or Rip.     

Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology

The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 (2007) 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.     

Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology

The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 (2007) 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.     

“Bouncing” of simple cosmological models with torsion

The known cosmological solutions of the Einstein-Cartan-Sciama-Kibble (ECSK) field equations are reviewed. The prevention of singularities is explained by means of the extension of the Hawking-Penrose singularity theorems to the ECSK theory. Singularity prevention in semiclassical “spinning dust” models derives from the postulated form of the canonical energy-momentum and spin angular momentum tensors for the matter distribution. The effects of shear, vorticity, and pressure are examined. The singularity behavior of cosmological models incorporating the Dirac field as the source of the metric and torsion is discussed. In these models one finds an enhancement, rather than a prevention of singularity formation. Finally, the consequences of spin and torsion for observational cosmology and for particle creation in the early universe are noted.     

Consequences of a Cosmological Phase Transition at the TeV Scale

A finite vacuum energy density implies the existence of a UV scale for gravitational modes. This gives a phenomenological scale to the dynamical equations governing the cosmological expansion that must satisfy constraints consistent with quantum measurability and spatial flatness. Examination of these constraints for the observed dark energy density establishes a time interval from the transition to the present, suggesting major modifications from the thermal equations of state far from Planck density scales. The assumption that a phase transition initiates the radiation dominated epoch is shown under several scenarios to be able to produce fluctuations to the CMB of the order observed. Quantum measurability constraints (eg. uncertainly relations) define cosmological scales bounded by luminal expansion rates. It is shown that the dark energy can consistently be interpreted as being due to the vacuum energy of collective gravitational modes which manifest as the zero-point motions of coherent Planck scale mass units prior to the UV scale onset of gravitational quantum de-coherence for the cosmology. A cosmological model with multiple scales, one of which replaces an apparent cosmological “constant”, is shown to reproduce standard cosmology during intermediate times, while making the exploration of the early and late time cosmology more accessible. Talk presented at the 2006 biennial conference of the International Association for Relativistic Dynamics, June 12–14, University of Connecticut (Storrs).     

Quantum Kaluza-Klein cosmologies (III)

The “ground state” proposal for the quantum state of the universe is generalized to the case of a noncompact spacelike three-hyperboloid as the configuration space. The most probable evolution of the universe must come from a gravitational instanton by quantum tunneling. We show that under some minisuperspace ansatz, there exists only S₄ × S₇ gravitational instanton in d = 11 supergravity. From the point of view of quantum cosmology this fact must be related to the fact that our observed spacetime is four-dimensional.     

Causal horizons in a bouncing universe

As our understanding of the past in a bouncing universe is limited, it becomes difficult to propose a cosmological model which can give some understanding of the causal structure of the bouncing universe. In this article we address the issue related to the particle horizon problem in the bouncing universe models. It is shown that in many models the particle horizon does not exist, and consequently the horizon problem is trivially solved. In some cases a bouncing universe can have a particle horizon and we specify the conditions for its existence. In the absence of a particle horizon the Hubble surface specifies the causal structure of a bouncing universe. We specify the complex relationship between the Hubble surface and the particle horizon when the particle horizon exists. The article also address the issue related to the event horizon in a bouncing universe. A toy example of a bouncing universe is first presented where we specify the conditions which dictate the presence of a particle horizon. Next we specify the causal structures of three widely used bouncing models. The first case is related to quintom matter bounce model, the second one is loop quantum cosmology based bounce model and lastly f(R) gravity induced bounce model. We present a brief discussion on the horizon problem in bouncing cosmologies. We point out that the causal structure of the various bounce models fit our general theoretical predictions.     

A 5D noncompact and non Ricci flat Kaluza–Klein Cosmology

A model universe is proposed in the framework of 5D noncompact Kaluza–Klein cosmology which is not Ricci flat. The 4D part as the Robertson–Walker metric is coupled to conventional perfect fluid, and its extra-dimensional part is coupled to a dark pressure through a scalar field. It is shown that neither early inflation nor current acceleration of the 4D universe would happen if the nonvacuum states of the scalar field would contribute to 4D cosmology.     

Insufficiency of the quantum state for deducing observational probabilities

It is usually assumed that the quantum state is sufficient for deducing all probabilities for a system. This may be true when there is a single observer, but it is not true in a universe large enough that there are many copies of an observer. Then the probability of an observation cannot be deduced simply from the quantum state (say as the expectation value of the projection operator for the observation, as in traditional quantum theory). One needs additional rules to get the probabilities. What these rules are is not logically deducible from the quantum state, so the quantum state itself is insufficient for deducing observational probabilities. This is the measure problem of cosmology.     

Investigation of the problem of singularities in general relativity

Recently Addy and Datta have obtained a linearized solution for isentropic motions of a perfect fluid by assigning Cauchy data on the hypersurfacex ⁴=0 and by imposing a restriction on the equation of state. In the present paper we pursue this study and discuss the problem of singularities from the standpoint of a local observer for which a singularity is defined as a state with an infinite proper rest mass density. It is shown that for a closed universe with any distribution of matter whatsoever there occurred a singularity in the past in the nonrotating parts of the universe and it must recur in the future. Furthermore, the collapse of a rotating fluid to a singularity seems inevitable when the relativistic equation of state is considered.