Closed Friedmann Universe Research Articles

Cosmological Constant (Λ); Fine Structure Constant (α) Two Results of Friedmann-Planck-Schwarzschild Models on Vacuum and Elementary Particles

This article presents in a synthetic way three articles published in JHEPGC ([1], [2]), EJAS [12] and develops some aspects.                  Two hypotheses are studied. In the first one, the vacuum is endowed with a quantum structure in which the vacuum particles are Friedmann-Planck micro-universes. For this, the article introduces a quantization of a closed Friedmann universe, then a quantization of the photon spheres filling this universe. This approach gives a numerical value consistent with cosmological measurements for the current dark energy density and the cosmological constant of our Universe.                Next, the second hypothesis takes the content of a model published in Physics Essays in 2013 [3], assuming that elementary particles are Schwarzschild photon spheres; these could be derived from the Friedmann photon spheres composing the vacuum particles. It is further recalled that the model presents a unified structure of elementary particles and allows us to calculate the value of the elementary electric charge and the fine structure constant. The masses of some elementary particles are calculated in a complementary model. Finally this article summarizes a model of closed cyclic universe described in reference [2].This universe begins as one alone Friedmann-Planck micro-universe, then multiplying to constitute our Universe. Further a Big-Rip suddenly transforms it into a Friedmann-Planck macro-universe on a much larger scale. This one is the beginning of a new Big-Bang with the same evolution as ours. This process can be assumed to explain the existence of the initial FP micro-universe: it would be the result of a Big-Rip at the end of the evolution of a much smaller scale universe.

Two Cosmological Hypotheses: The Friedmann-Planck Micro-Universes for Vacuum Particles, The Schwarzschild Photon Spheres for Elementary Particles

This article presents in a synthetic way two articles published in JHEPGC ([1], [2]) and develops some aspects. Two hypotheses are studied. In the first one, the vacuum is endowed with a quantum structure in which the vacuum particles are Friedmann-Planck micro-universes. For this, the article introduces a quantization of a closed Friedmann universe, then a quantization of the photon spheres filling this universe. This approach gives a numerical value consistent with cosmological measurements for the current dark energy density of our Universe. Next, the second hypothesis takes the content of a model published in Physics Essays in 2013 [3], assuming that elementary particles are Schwarzschild photon spheres; these could be derived from the Friedmann photon spheres composing the vacuum particles. It is further recalled that the model presents a unified structure of elementary particles and allows us to calculate the value of the elementary electric charge as well as the mass of the elementary particles. Finally this article summarizes a model of closed universe described in reference [2]

Remarks on Some Results Related to the Thermal Casimir Effect in Einstein and Closed Friedmann Universes with a Cosmic String

In this paper, we present a review of some recent results concerning the thermal corrections to the Casimir energy of massless scalar, electromagnetic, and massless spinor fields in the Einstein and closed Friedmann universes with a cosmic string. In the case of a massless scalar field, it is shown that the Casimir energy can be written as a simple sum of two terms; the first one corresponds to the Casimir energy for the massless scalar field in the Einstein and Friedmann universes without a cosmic string, whereas the second one is simply the Casimir energy of the electromagnetic field in these backgrounds, multiplied by a parameter λ=(1/α)−1, where α is a constant that codifies the presence of the cosmic string, and is related to its linear mass density, μ, by the expression α=1−Gμ. The Casimir free energy and the internal energy at a temperature different from zero, as well as the Casimir entropy, are given by similar sums. In the cases of the electromagnetic and massless spinor fields, the Casimir energy, free energy, internal energy, and Casimir entropy are also given by the sum of two terms, similarly to the previous cases, but now with both terms related to the same field. Using the results obtained concerning the mentioned thermodynamic quantities, their behavior at high and low temperatures limits are studied. All these results are particularized to the scenario in which the cosmic string is absent. Some discussions concerning the validity of the Nernst heat theorem are included as well.

Perturbations and linearization stability of closed Friedmann universes

We consider perturbations of closed Friedmann universes. Perturbation modes of two lowest wavenumbers ($L=0$ and $1$) are generally known to be fictitious, but here we show that both are physical. The issue is more subtle in Einstein static universes where closed background space has a time-like Killing vector with the consequent occurrence of linearization instability. Proper solutions of the linearized equation need to satisfy the Taub constraint on a quadratic combination of first-order variables. We evaluate the Taub constraint in the two available fundamental gauge conditions, and show that in both gauges the $L\geq 1$ modes should accompany the $L=0$ (homogeneous) mode for vanishing sound speed, $c_{s}$. For $c_{s}^{2}>1/5$ (a scalar field supported Einstein static model belongs to this case with $c_s^2 = 1$), the $L\geq 2$ modes are known to be stable. In order to have a stable Einstein static evolutionary stage in the early universe, before inflation and without singularity, although the Taub constraint does not forbid it, we need to find a mechanism to suppress the unstable $L=0$ and $L=1$ modes.

Euclidean wormholes in Hořava-Lifshitz gravity

Euclidean wormholes first appeared in the Euclidean path integral approach to quantum gravity. In a more general way, Hawking and Page interpreted such configurations as solutions to the Wheeler-DeWitt equation with appropriate boundary conditions. We study Euclidean wormholes in the framework of the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz theory of gravity. We use its projectable version to obtain the Wheeler-DeWitt equation of a minisuperspace model considering a closed Friedmann Universe with a massless scalar field. For large values of the scale factor we find that the solution of the Wheeler-DeWitt equation coincides with the one obtained by Hawking. Whereas in the limit corresponding to the early Universe we find a new set of solutions, which agree with the Hawking and Page boundary conditions for wormholes.

Hypotheses on Vacuum and Elementary Particles: The Friedmann-Planck Micro-Universe, Friedmann and Schwarzschild Photon Spheres

This article presents the hypothesis that the vacuum is endowed with a quantum structure; the vacuum particles would be Friedmann-Planck micro-universes. For this, the article introduces a quantization of a closed Friedmann universe, then a quantization of the photon spheres filling this universe. This approach gives a numerical value consistent with cosmological measurements for the current dark energy density of our Universe. Next, the article takes the content of a model published in Physics Essays in 2013 [1], assuming that elementary particles are Schwarzschild photon spheres; these could be derived from the Friedmann photon spheres composing the vacuum particles. It is further recalled that the model presents a unified structure of elementary particles and allows us to calculate the value of the elementary electric charge as well as the mass of the elementary particles.

WKB approximation for a deformed Schrodinger-like equation and its applications to quasinormal modes of black holes and quantum cosmology

In this paper, we use the WKB approximation method to approximately solve a deformed Schrodinger-like differential equation: [−ħ2∂ξ2g2(−iħα∂ξ)−p2(ξ)]ψ(ξ)=0, which are frequently dealt with in various effective models of quantum gravity, where the parameter α characterizes effects of quantum gravity. For an arbitrary function g(x) satisfying several properties proposed in the paper, we find the WKB solutions, the WKB connection formulas through a turning point, the deformed Bohr–Sommerfeld quantization rule, and the deformed tunneling rate formula through a potential barrier. Several examples of applying the WKB approximation to the deformed quantum mechanics are investigated. In particular, we calculate the bound states of the Pöschl–Teller potential and estimate the effects of quantum gravity on the quasinormal modes of a Schwarzschild black hole. Moreover, the area quantum of the black hole is considered via Bohr's correspondence principle. Finally, the WKB solutions of the deformed Wheeler–DeWitt equation for a closed Friedmann universe with a scalar field are obtained, and the effects of quantum gravity on the probability of sufficient inflation is discussed in the context of the tunneling proposal.

On the Magnetic Evolution in Friedmann Universes and the Question of Cosmic Magnetogenesis

We analyse the evolution of primordial magnetic fields in spatially flat Friedmann universes and reconsider the belief that, after inflation, these fields decay adiabatically on all scales. Without abandoning classical electromagnetism or standard cosmology, we demonstrate that this is not necessarily the case for superhorizon-sized magnetic fields. The underlying reason for this is causality, which confines the post-inflationary process of electric-current formation, electric-field elimination and magnetic-flux freezing within the horizon. As a result, the adiabatic magnetic decay is not a priori guaranteed on super-Hubble scales. Instead, after inflation, large-scale magnetic fields obey a power-law solution, where one of the modes drops at a rate slower than the adiabatic. Whether this slowly decaying mode can dominate and dictate the post-inflationary magnetic evolution depends on the initial conditions. These are determined by the evolution of the field during inflation and by the nature of the transition from the de Sitter phase to the reheating era and then to the subsequent epochs of radiation and dust. We discuss two alternative and complementary scenarios to illustrate the role and the implications of the initial conditions for cosmic magnetogenesis. Our main claim is that magnetic fields can be superadiabatically amplified after inflation, as long as they remain outside the horizon. This means that inflation-produced fields can reach astrophysically relevant residual strengths without breaking away from standard physics. Moreover, using the same causality arguments, one can constrain (or in some cases assist) the non-conventional scenarios of primordial magnetogenesis that amplify their fields during inflation. Finally, we show that our results extend naturally to the marginally open and the marginally closed Friedmann universes.

Loop quantum cosmology with self-dual variables

Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann universe coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by choosing a particular inner product for the kinematical Hilbert space. While holonomies of the self-dual Ashtekar connection are not well-defined in the kinematical Hilbert space, it is possible to introduce a family of generalized holonomy-like operators of which some are well-defined; these operators in turn are used in the definition of the Hamiltonian constraint operator where the scalar field can be used as a relational clock. The resulting quantum theory is closely related, although not identical, to standard loop quantum cosmology constructed from the Ashtekar-Barbero variables with a real Immirzi parameter. Effective Friedmann equations are derived, which provide a good approximation to the full quantum dynamics for sharply-peaked states whose volume remains much larger than the Planck volume, and they show that for these states quantum gravity effects resolve the big-bang and big-crunch singularities and replace them by a non-singular bounce. Finally, the loop quantization in self-dual variables of a flat Friedmann space-time is recovered in the limit of zero spatial curvature and is identical to the standard loop quantization in terms of the real-valued Ashtekar-Barbero variables.

Topological thermal Casimir effect for spinor and electromagnetic fields

We obtain the thermal corrections to the Casimir energy for the neutrino and electromagnetic fields in Einstein and closed Friedmann universes containing a static, infinitely straight and thin cosmic string. The Casimir free energy is also obtained as well as their low and high temperature limits. It is shown that the vacuum energies associated with these fields, in the background considered, are given simply by the vacuum energies in the absence of the cosmic string multiplied by a factor that codifies the presence of this topological defect.

Criticality and big brake singularities in the tachyonic evolutions of closed Friedmann universes with cold dark matter

The evolution of a closed Friedmann universe filled by a tachyon scalar field with a trigonometric potential and cold dark matter (CDM) is investigated. A subset of the evolutions consistent to 1$\sigma $ confidence level with the Union 2.1 supernova data set is identified. The evolutions of the tachyon field are classified. Some of them evolve into a de Sitter attractor, while others proceed through a pseudo-tachyonic regime into a sudden future singularity. Critical evolutions leading to Big Brake singularities in the presence of CDM are found and a new type of cosmological evolution characterized by singularity avoidance in the pseudo-tachyon regime is presented.

Quantum cosmology, minimal length, and holography

We study the effects of a generalized uncertainty principle on the classical and quantum cosmology of a closed Friedmann Universe whose matter content is either a dust or a radiation fluid. More concretely, assuming the existence of a minimal length, we show that the entropy will constitute a Dirac observable. In addition, 't Hooft conjecture on the cosmological holographic principle is also investigated. We describe how this holographic principle is satisfied for large values of a quantum number, $n$. This occurs when the entropy is computed in terms of the minimal area.

Dirac observables and boundary proposals in quantum cosmology

We study the reduced phase space quantization of a closed Friedmann Universe, where matter content is constituted by two (no-interacting) fluids, namely dust (or cold dark matter) and radiation. It is shown that, for this particular model, specific boundary conditions can be related to the algebra of Dirac observables.

Supermassive Black Holes, Large Scale Structure and Holography

This analysis considers our universe as a closed Friedmann universe, dominated by vacuum energy in the form of a cosmological constant, with cosmological parameters obtained from full mission Planck satellite observations. A few simple assumptions lead to straightforward calculation of general features of large scale structures in the universe and minimum stellar mass as a function of redshift. Those assumptions also generate upper and lower bounds on supermassive black hole mass in relation to total stellar mass of the host galaxy, consistent with observations across four orders of magnitude of black hole mass and five orders of magnitude of galactic stellar mass. The results are based only on fundamental constants and measured cosmological parameters. No arbitrary parameters are involved.

THE PROBLEM OF INERTIA IN FRIEDMANN UNIVERSES

In this paper we study the origin of inertia in a curved spacetime, particularly the spatially flat, open and closed Friedmann universes. This is done using Sciama's law of inertial induction, which is based on Mach's principle, and expresses the analogy between the retarded far fields of electrodynamics and those of gravitation. After obtaining covariant expressions for electromagnetic fields due to an accelerating point charge in Friedmann models, we adopt Sciama's law to obtain the inertial force on an accelerating mass m by integrating over the contributions from all the matter in the universe. The resulting inertial force has the form F = -kma, where k < 1 depends on the choice of the cosmological parameters such as ΩM, ΩΛ and ΩR and is also redshift-dependent.

Thermal Casimir effect in closed Friedmann universe revisited

We reconsider Casimir free energy and internal energy at nonzero temperature in the static Einstein and closed Friedmann universe. It is shown that the Casimir free energy is given by the difference between the free energy of a topologically nontrivial manifold and a tangential Minkowski space-time. We derive exact expressions for the Casimir free energy, internal energy and pressure in Einstein and Friedmann universes in terms of single sums. The Casimir entropy is shown to satisfy the Nernst heat theorem. Exact expressions for corresponding total quantities in the Einstein universe are obtained from the Casimir ones by adding a contribution of the black-body radiation. The asymptotic expressions for the Casimir free energy and internal energy at both high and low temperature are shown to be in direct analogy with those for two ideal-metal plates and an ideal-metal spherical shell. Specifically, at high temperature the classical limit holds.

Energy-momentum of the Friedmann models in General Relativity and the teleparallel theory of gravity

This paper is devoted to the evaluation of the energy-momentum density components for the Friedmann models. For this purpose, we have used Møller’s pseudotensor prescription in General Relativity and a certain energy-momentum density developed from Møller’s teleparallel formulation. We show that the energy density of the closed Friedmann universe vanishes on the spherical shell at the radius ρ = 2[Formula: see text]. This coincides with the earlier results available in the literature. We also discuss the energy of the flat and open models. A comparison shows a partial consistency between Møller’s pseudotensor for General Relativity and teleparallel theory. Further, we show that the results are independent of the free dimensionless coupling constant of the teleparallel gravity.PACS No.: 04.20.–q

Simple quantum cosmology: vacuum energy and initial state

A static non-singular 10-dimensional closed Friedmann universe of Planck size, filled with a perfect fluid with equation of state p = − $\frac{2}{3}$ ε, can arise spontaneously by a quantum fluctuation from nothing in 11-dimensional spacetime. A quantum transition from this state can initiate the inflationary quantum cosmology outlined in [Gen. Relativ. Gravit. 33, 1415 (2001)]. With no fine-tuning, that cosmology predicts about 60 e-folds of inflation and a vacuum energy density depending only on the number of extra space dimensions (seven), G,ℏ, c and the ratio between the strength of gravity and the strength of the strong force. The fraction of the total energy in the universe represented by this vacuum energy depends on the Hubble constant H0. Estimates of H0 from WMAP, SDSS, the Hubble Key Project, and Sunyaev-Zeldovich and X-ray flux measurements range from 60 to 72 km s−1 Mpc−1. Using a mid-range value of H0 = 65 km s−1 Mpc−1, the model in [Gen. Relativ. Gravit. 33, 1415 (2001)] predicts Ω Λ≈ 0.7.

Quantum time evolution of a closed Friedmann model

We consider a quantized dust-filled closed Friedmann universe in Ashtekar-type variables. Due to the presence of matter, the ‘timelessness problem’ of quantum gravity can be solved in this case by using the following approach to the Hamiltonian operator.The arising Wheeler–DeWitt equation appears as an eigenvalue equation for discrete values of the total mass.Its gravitational part is considered as the generator of the time evolution of geometry.Superpositions of different eigenfunctions with time behaviour governed by the corresponding eigenvalues of mass are admitted.Following these lines, a time evolution with a correct classical limit is obtained.

Tunneling of the Closed Friedmann Universe with Generation of Scalar Waves

The evolution of the closed Friedmann Universe with a packet of short scalar waves is considered with the help of the Wheeler--DeWitt equation. The packet ensures conservation of homogeneity and isotropy of the metric on average. It is shown that during tunneling the amplitudes of short waves of a scalar field can increase catastrophically promptly if their influence to the metric do not take into account. This effect is similar to the Rubakov-effect of catastrophic particle creation calculated already in 1984. In our approach to the problem it is possible to consider self-consistent dynamics of the expansion of the Universe and amplification of short waves. It results in a decrease of the barrier and interruption of amplification of waves, and we get an exit of the wave function from the quantum to the classically available region.