CONNECTING THE NONSINGULAR ORIGIN OF THE UNIVERSE, THE VACUUM STRUCTURE AND THE COSMOLOGICAL CONSTANT PROBLEM

We consider a nonsingular origin for the universe starting from an Einstein static universe, the so-called "emergent universe" scenario, in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field ϕ are considered in the action. The first-order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (SSB) of scale invariance (SI). After SSB of SI, it is found that a nontrivial potential for the dilaton is generated. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe, followed by an inflationary phase and ϕ → -∞, describing our present universe. The dynamics of the scalar field becomes nonlinear and these nonlinearities produce a nontrivial vacuum structure for the theory and are responsible for the stability of some of the emergent universe solutions, which exists for a parameter range of values of the vacuum energy in ϕ → -∞, which must be positive but not very big, avoiding the extreme fine tuning required to keep the vacuum energy density of the present universe small. The nontrivial vacuum structure is crucial to ensure the smooth transition from the emerging phase, to an inflationary phase and finally to the slowly accelerated universe now. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.

Download Full-text

NONSINGULAR ORIGIN OF THE UNIVERSE AND ITS PRESENT VACUUM ENERGY DENSITY

International Journal of Modern Physics A ◽

10.1142/s0217751x11053614 ◽

2011 ◽

Vol 26 (17) ◽

pp. 2951-2972 ◽

Cited By ~ 9

Author(s):

E. I. GUENDELMAN

Keyword(s):

Energy Density ◽

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Scale Invariance ◽

Vacuum Energy ◽

Vacuum Energy Density ◽

Emergent Universe ◽

Present Universe ◽

The Universe ◽

Origin Of The Universe

We consider a nonsingular origin for the universe starting from an Einstein static universe, the so-called "emergent universe" scenario, in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field ϕ are considered in the action. The first-order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking of scale invariance. After spontaneous symmetry breaking of scale invariance it is found that a nontrivial potential for the dilaton is generated. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe, followed by an inflationary phase and ϕ → - ∞, describing our present universe. The dynamics of the scalar field becomes nonlinear and these nonlinearities are instrumental in the stability of some of the emergent universe solutions, which exists for a parameter range of values of the vacuum energy in ϕ → - ∞, which must be positive but not very big, avoiding the extreme fine tuning required to keep the vacuum energy density of the present universe small. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.

Download Full-text

Do we come from a quantum anomaly?

International Journal of Modern Physics D ◽

10.1142/s0218271819440024 ◽

2019 ◽

Vol 28 (14) ◽

pp. 1944002 ◽

Cited By ~ 9

Author(s):

Spyros Basilakos ◽

Nick E. Mavromatos ◽

Joan Solà Peracaula

Keyword(s):

Dark Matter ◽

Dark Energy ◽

Energy Density ◽

Hubble Parameter ◽

Vacuum Energy ◽

Vacuum Energy Density ◽

Quantum Anomaly ◽

Inflationary Phase ◽

Axion Field ◽

The Universe

We present a string-based picture of the cosmological evolution in which (CP-violating) gravitational anomalies acting during the inflationary phase of the universe cause the vacuum energy density to “run” with the effective Hubble parameter squared, [Formula: see text], thanks to the axion field of the bosonic string multiplet. This leads to baryogenesis through leptogenesis with massive right-handed neutrinos. The generation of chiral matter after inflation helps in cancelling the anomalies in the observable radiation- and matter-dominated eras. The present era inherits the same “running vacuum” structure triggered during the inflationary time by the axion field. The current dark energy is thus predicted to be mildly dynamical, and dark matter should be made of axions. Paraphrasing Carl Sagan [ https://www.goodreads.com/author/quotes/10538.Carl_Sagan .]: we are all anomalously made from starstuff.

Download Full-text

NONSINGULAR ORIGIN OF THE UNIVERSE AND THE COSMOLOGICAL CONSTANT PROBLEM

International Journal of Modern Physics D ◽

10.1142/s0218271811020718 ◽

2011 ◽

Vol 20 (14) ◽

pp. 2767-2771 ◽

Cited By ~ 3

Author(s):

E. I. GUENDELMAN

Keyword(s):

Vacuum Energy ◽

Zero Point ◽

Vacuum Energy Density ◽

Cosmological Constant Problem ◽

Static Universe ◽

First Order ◽

Present Universe ◽

Einstein Static Universe ◽

The Universe ◽

Origin Of The Universe

We consider a nonsingular origin for the universe starting from an Einstein static universe in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, also curvature, curvature square terms, first order formalism and for scale invariance a dilaton field ϕ are considered in the action. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe and ϕ → -∞, describing our present universe. Surprisingly, avoidance of singularities and stability as ϕ → ∞ imply a positive but small vacuum energy as ϕ → -∞. Zero vacuum energy density for the present universe is the "threshold" for universe creation.

Download Full-text

Particle Phase Transitions can Prevent an Initial Cosmological Singularity

Symposium - International Astronomical Union ◽

10.1017/s0074180900039504 ◽

1983 ◽

Vol 104 ◽

pp. 447-451

Author(s):

S. A. Bludman

Keyword(s):

Energy Density ◽

Vacuum Energy ◽

Initial Singularity ◽

Minimum Size ◽

Maximum Temperature ◽

Vacuum Energy Density ◽

Particle Phase ◽

Cosmological Singularity ◽

Present Universe ◽

The Universe

The present universe has small vacuum energy density (cosmological constant) and small spatial curvature. Therefore, before symmetry breaking, it had to have huge positive vacuum energy density, significant curvature, and low entropy. Because the energy positivity condition was not then satisfied, there need not have been an initial singularity (Hot Big Bang). If the universe is spatially open or the initial entropy high enough, then before the elementary particle phase transition, it was indeed an inflecting universe with an initial singularity. But if the universe is spatially closed and of low initial entropy, it needed to be a curvature-dominated bouncing universe, with a minimum size and maximum temperature (Tepid Little Bang). The closure of the present universe will therefore determine whether or not there was an initial singularity.

Download Full-text

BAGS AND CONFINEMENT GOVERNED BY SPONTANEOUS SYMMETRY BREAKING OF SCALE INVARIANCE

International Journal of Modern Physics A ◽

10.1142/s0217751x10050305 ◽

2010 ◽

Vol 25 (22) ◽

pp. 4195-4220 ◽

Cited By ~ 12

Author(s):

E. I. GUENDELMAN

Keyword(s):

Energy Density ◽

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Gauge Field ◽

Scale Invariance ◽

Vacuum Energy ◽

Equations Of Motion ◽

Flat Space ◽

Vacuum Energy Density ◽

Conformally Invariant

A general coordinate invariant theory is constructed where confinement of gauge fields and gauge dynamics in general is governed by the spontaneous symmetry breaking (s.s.b.) of scale invariance. The model uses two measures of integration in the action, the standard [Formula: see text] where g is the determinant of the metric and another measure Φ independent of the metric. To implement scale invariance, a dilaton field is introduced. Using the first-order formalism, curvature (ΦR and [Formula: see text]) terms, gauge field term ([Formula: see text] and [Formula: see text]) and dilaton kinetic terms are introduced in a conformally invariant way. Exponential potentials for the dilaton break down (softly) the conformal invariance down to global scale invariance, which also suffers s.s.b. after integrating the equations of motion. The model has a well-defined flat space limit. As a result of the s.s.b. of scale invariance phases with different vacuum energy density appear. Inside the bags, that is in the regions of larger vacuum energy density, the gauge dynamics is normal, that is nonconfining, while for the region of smaller vacuum energy density, the gauge field dynamics is confining. Likewise, the dynamics of scalars, like would be Goldstone bosons, is suppressed inside the bags.

Download Full-text

Application of Self-Similar Symmetry Model to Dark Energy

10.20944/preprints201804.0348.v1 ◽

2018 ◽

Cited By ~ 2

Author(s):

Tomohide Sonoda

Keyword(s):

Dark Energy ◽

Energy Density ◽

Vacuum Energy ◽

Structure Constant ◽

Fine Tuning ◽

Theoretical Modelling ◽

Fine Structure Constant ◽

Vacuum Energy Density ◽

Self Similar ◽

The Universe

Recent observations of the dark energy density demonstrates the fine-tuning problem and challenges in theoretical modelling. In this study, we apply the self-similar symmetry (SSS) model, describing the hierarchical structure of the universe based on the Dirac large numbers hypothesis, to Einstein's cosmological term. We introduce a new similarity dimension, DB, in the SSS model. Using the DB SSS model, the cosmological constant, vacuum energy density, and Hubble parameter can be simply expressed as a function of the cosmic microwave background (CMB) temperature. We show that the initial value of the vacuum energy density at the creation of the universe is ρ0 = 1/8παf6, where αf is the fine structure constant. The results indicate that the CMB is the primary factor for the evolution of the universe, providing a unified understanding of the problems of naturalness.

Download Full-text

The evolution of the universe in asymmetric cosmic time

Advances in Theoretical & Computational Physics ◽

10.33140/atcp.04.03.01 ◽

2021 ◽

Vol 4 (3) ◽

Keyword(s):

Energy Density ◽

Nuclear Force ◽

Vacuum Energy ◽

Cosmic Time ◽

Big Bang ◽

Vacuum Energy Density ◽

De Sitter ◽

Planck Time ◽

The Big Bang ◽

The Universe

The Cosmic Time Hypothesis (CTH) presented in this paper is a purely axiomatic theory. In contrast to today's standard model of cosmology, the ɅCDM model, it does not contain empirical parameters such as the cosmological constant Ʌ, nor does it contain sub-theories such as the inflation theory. The CTH was developed solely on the basis of the general theory of relativity (GRT), aiming for the greatest possible simplicity. The simplest cosmological model permitted by ART is the Einstein-de Sitter model. It is the basis for solving some of the fundamental problems of cosmology that concern us today. First of all, the most important results of the CTH: It solves one of the biggest problems of cosmology the problem of the cosmological constant (Ʌ)-by removing the relation between and the vacuum energy density ɛv (Λ=0, ɛv > 0). According to the CTH, the vacuum energy density ɛv is not negative and constant, as previously assumed, but positive and time-dependent (ɛv ̴ t -2). ɛv is part of the total energy density (Ɛ) of the universe and is contained in the energy-momentum tensor of Einstein's field equations. Cosmology is thus freed from unnecessary ballast, i.e. a free parameter (= natural constant) is omitted (Ʌ = 0). Conclusion: There is no "dark energy"! According to the CTH, the numerical value of the vacuum energy density v is smaller by a factor of ≈10-122 than the value calculated from quantum field theory and is thus consistent with observation. The measurement data obtained from observations of SNla supernovae, which suggest a currently accelerated expansion of the universe, result - if interpreted from the point of view of the CTH - in a decelerated expansion, as required by the Einstein-de Sitter universe. Dark matter could also possibly not exist, because the KZH demands that the "gravitational constant" is time-dependent and becomes larger the further the observed objects are spatially and thus also temporally distant from us. Gravitationally bound local systems, e.g. Earth - Moon or Sun - Earth, expand according to the same law as the universe. This explains why Hubble's law also applies within very small groups of galaxies, as observations show. The CTH requires that the strongest force (strong nuclear force) and the weakest (gravitational force) at Planck time (tp ≈10-43 seconds after the "big bang") when all forces of nature are supposed to have been united in a single super force, were of equal magnitude and had the same range. According to the KZH, the product of the strength and range of the gravitational force is constant, i.e. independent of time, and is identical to the product of the strength and range of the strong nuclear force. At Planck time, the universe had the size of an elementary particle (Rp = rE ≈10-15 m). This value also corresponds to the range of the strong nuclear force (Yukawa radius) and the Planck length at Planck time. The CTH provides a possible explanation for Mach's first and second principles. It solves some old problems of the big bang theory in a simple and natural way. The problem of the horizon, flatness, galaxy formation and the age of the world. The inflation theory thus becomes superfluous. • The CTH provides the theoretical basis for the theory of Earth expansion • In Cosmic Time, there was no Big Bang. The universe is infinitely old. • Unlike other cosmological models, the CTH does not require defined "initial conditions" because there was no beginning. • The CTH explains why the cosmic expansion is permanently in an unstable state of equilibrium, which is necessary for a long-term flat (Euclidean), evolutionarily developing universe.

Download Full-text

Vacuum energy and the cosmological constant

Modern Physics Letters A ◽

10.1142/s0217732315400337 ◽

2015 ◽

Vol 30 (22) ◽

pp. 1540033 ◽

Cited By ~ 5

Author(s):

Steven D. Bass

Keyword(s):

Energy Density ◽

Large Hadron Collider ◽

Cosmological Constant ◽

Vacuum Energy ◽

Hadron Collider ◽

Planck Scale ◽

Vacuum Energy Density ◽

Accelerating Expansion ◽

Expansion Of The Universe ◽

The Universe

The accelerating expansion of the Universe points to a small positive value for the cosmological constant or vacuum energy density. We discuss recent ideas that the cosmological constant plus Large Hadron Collider (LHC) results might hint at critical phenomena near the Planck scale.

Download Full-text

Quantum Mechanical Explanation for Dark Energy, Cosmic Coincidence, Flatness, Age, and Size of the Universe

Open Astronomy ◽

10.1515/astro-2019-0021 ◽

2019 ◽

Vol 28 (1) ◽

pp. 220-227 ◽

Cited By ~ 1

Author(s):

Biswaranjan Dikshit

Keyword(s):

Dark Energy ◽

Energy Density ◽

Vacuum Energy ◽

Vacuum Energy Density ◽

Quantum Mechanical ◽

Coincidence Problem ◽

Astronomical Observations ◽

The Universe ◽

Matter Energy ◽

Cosmic Coincidence Problem

Abstract One of the most important problems in astronomy is the cosmological constant problem in which conventional calculation of vacuum energy density using quantum mechanics leads to a value which is ~10123 times more than the vacuum energy estimated from astronomical observations of expanding universe. The cosmic coincidence problem questions why matter energy density is of the same order of magnitude as the vacuum energy density at present time. Finally, the mechanism responsible for spatial flatness is not clearly understood. In this paper, by taking the vacuum as a finite and closed quantum oscillator, we solve all of the above-mentioned problems. At first, by using the purely quantum mechanical approach, we predict that the dark energy density is c4/(GR2) = 5.27×10−10 J/m3 (where R is radius of 3-sphere of the universe) and matter energy density is c4/(2GR2) = 2.6×10−10 J/m3 which match well with astronomical observations. We also prove that dark energy has always been ~66.7% and matter energy has been ~33.3% of the total energy and thus solve the cosmic coincidence problem. Next, we show how flatness of space could be maintained since the early stage of the universe. Finally, using our model, we derive the expression for age and radius of the universe which match well with the astronomical data.

Download Full-text