Energy scale of inflation from the recurrence time of the universe

2015 ◽  
Vol 24 (03) ◽  
pp. 1550026
Author(s):  
K. Ropotenko
Keyword(s):  
Cosmological Constant ◽  
Planck Scale ◽  
Energy Scale ◽  
Recurrence Time ◽  
Inflationary Universe ◽  
De Sitter ◽  
Cosmological Constant Problem ◽  
The Universe

It is shown that the de Sitter equilibrium cosmology predicts the energy scale of inflation that significantly exceeds the Planck scale. An alternative calculation of the probability for a fluctuation into an inflationary universe is proposed which gives a more realistic energy scale of inflation. An interpretation of the cosmological constant problem in the de Sitter equilibrium cosmology is briefly discussed.

BLACK HOLE QUANTIZATION, THERMODYNAMICS AND COSMOLOGICAL CONSTANT

2004 ◽  
Vol 13 (05) ◽  
pp. 885-898
Author(s):  
LI XIANG
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Planck Scale ◽  
Additional Term ◽  
Logarithmic Correction ◽  
De Sitter ◽  
Horizon Area ◽  
Constant Distance ◽  
The Universe

Bekenstein argues that the horizon area of a black hole has a constant distance spectrum. We investigate the effects of such a discrete spectrum on the thermodynamics of a Schwarzchild black hole (SBH) and a Schwarzchild–de Sitter black hole (SdBH), in terms of the time-energy uncertainty relation and Stefan–Boltzman law. For the massive SBH, a negative and logarithmic correction to the Bekenstein–Hawking entropy is obtained, as well as other authors by using other methods. As to the minimal hole near the Planck scale, its entropy is no longer proportional to the horizon area, but is of order of the mass of the hole. This is similar to an excited stringy state. The vanishing heat capacity of such a minimal black hole implies that it may be a remnant as the ground state of the evaporating hole. The properties of a SdBH are similar to the SBH, except for an additional term of square area associated with the cosmological constant. In order to maintain the validity of the Bekenstein–Hawking formula, the cosmological constant is strongly limited by the size of the biggest black hole in the universe. A relation associated with the cosmological constant, Planck area and the Stefan–Boltzman constant is obtained. The cosmological constant is not only related to the vacuum energy, but is also related to the thermodynamics.

scholarly journals New quantum phase of the Universe before inflation and its cosmological and dark energy implications

2019 ◽  
Vol 34 (27) ◽  
pp. 1950155
Author(s):  
Norma G. Sanchez
Keyword(s):  
Dark Energy ◽  
Cosmological Constant ◽  
Quantum Physics ◽  
Planck Scale ◽  
De Sitter ◽  
Quantum Domain ◽  
Wave Particle Duality ◽  
Classical Quantum ◽  
De Sitter Universe ◽  
The Universe

The physical history of the Universe is completed by including the quantum Planckian and trans-Planckian phase before inflation in the Standard Model of the Universe in agreement with observations. In the absence of a complete quantum theory of gravity, we start from quantum physics and its foundational milestone. The universal classical-quantum (or wave-particle) duality, which we extend to gravity and the Planck domain. As a consequence, classical, quantum Planckian and super-Planckian regimes are covered, and the usual quantum domain as well. A new quantum precursor phase of the Universe appears beyond the Planck scale [Formula: see text]: [Formula: see text]; the known classical/semiclassical Universe being in the range: [Formula: see text]. We extend in this way the de Sitter Universe to the quantum domain: classical-quantum de Sitter duality. As a result: (i) The classical and quantum dual de Sitter temperatures and entropies are naturally included, and the different (classical, semiclassical, quantum Planckian and trans-Planckian) de Sitter regimes characterized in a precise and unifying way. (ii) We apply it to relevant cosmological examples as the CMB, inflation and dark energy. This allows us to find in a simple and consistent way. (iii) Full quantum inflationary spectra and their CMB observables, including in particular the classical known inflation spectra and the quantum corrections to them. (iv) A whole unifying picture for the Universe epochs and their quantum precursors emerges with the cosmological constant as the vacuum energy, entropy and temperature of the Universe, clarifying the so-called cosmological constant problem which once more in its rich history needed to be revised.

scholarly journals The nature of the gravitational vacuum

2019 ◽  
Vol 28 (14) ◽  
pp. 1944005
Author(s):  
Samir D. Mathur
Keyword(s):  
Black Hole ◽  
String Theory ◽  
Cosmological Constant ◽  
Mass Formula ◽  
Vacuum Energy ◽  
Planck Scale ◽  
Cosmological Constant Problem ◽  
Horizon Radius ◽  
Number Formula ◽  
Gravitational Vacuum

The vacuum must contain virtual fluctuations of black hole microstates for each mass [Formula: see text]. We observe that the expected suppression for [Formula: see text] is counteracted by the large number [Formula: see text] of such states. From string theory, we learn that these microstates are extended objects that are resistant to compression. We argue that recognizing this ‘virtual extended compression-resistant’ component of the gravitational vacuum is crucial for understanding gravitational physics. Remarkably, such virtual excitations have no significant effect for observable systems like stars, but they resolve two important problems: (a) gravitational collapse is halted outside the horizon radius, removing the information paradox, (b) spacetime acquires a ‘stiffness’ against the curving effects of vacuum energy; this ameliorates the cosmological constant problem posed by the existence of a planck scale [Formula: see text].

scholarly journals Variation of the fundamental constants over the cosmological time: veracity of Dirac’s intriguing hypothesis

2016 ◽  
Vol 94 (1) ◽  
pp. 89-94 ◽  
Author(s):  
Cláudio Nassif ◽  
A.C. Amaro de Faria
Keyword(s):  
Fine Structure ◽  
Early Universe ◽  
Early Period ◽  
Planck Scale ◽  
Structure Constant ◽  
Energy Scale ◽  
Fine Structure Constant ◽  
Cosmological Time ◽  
Age Of The Universe ◽  
The Universe

We investigate how the universal constants, including the fine structure constant, have varied since the early universe close to the Planck energy scale (EP ∼ 1019 GeV) and, thus, how they have evolved over the cosmological time related to the temperature of the expanding universe. According to a previous paper (Nassif and Amaro de Faria, Jr. Phys. Rev. D, 86, 027703 (2012). doi:10.1103/PhysRevD.86.027703), we have shown that the speed of light was much higher close to the Planck scale. In the present work, we will go further, first by showing that both the Planck constant and the electron charge were also too large in the early universe. However, we conclude that the fine structure constant (α ≅ 1/137) has remained invariant with the age and temperature of the universe, which is in agreement with laboratory tests and some observational data. Furthermore, we will obtain the divergence of the electron (or proton) mass and also the gravitational constant (G) at the Planck scale. Thus, we will be able to verify the veracity of Dirac’s belief about the existence of “coincidences” between dimensionless ratios of subatomic and cosmological quantities, leading to a variation of G with time, that is, the ratio of the electrostatic to gravitational forces between an electron and a proton (∼1041) is roughly equal to the age of the universe divided by an elementary time constant, so that the strength of gravity, as determined by G, must vary inversely with time in the approximation of lower temperature or for times very far from the early period, to compensate for the time-variation of the Hubble parameter (H ∼ t−1). In short, we will show the validity of Dirac’s hypothesis only for times very far from the early period or T ≪ TP (∼1032 K).

scholarly journals ON THE COSMOLOGICAL CONSTANT PROBLEM

1996 ◽  
Vol 05 (04) ◽  
pp. 433-440 ◽  
Author(s):  
DHURJATI PRASAD DATTA
Keyword(s):  
Cosmological Constant ◽  
Mechanical Model ◽  
Vacuum Energy ◽  
Quantum Mechanical ◽  
Cosmological Constant Problem ◽  
Molecular Physics ◽  
Simple Quantum ◽  
Time Formalism ◽  
Oppenheimer Approximation ◽  
The Universe

A simple quantum mechanical model of a closed interacting system is studied following the intrinsic time formalism developed recently, on the basis of the modified Born-Oppenheimer approximation. Apart from shedding further insights into the recent results on a possible nongravitating vacuum energy in the universe, the study also offers potentially interesting possibilities even in atomic/molecular physics.

scholarly journals THE POINCARÉ CONJECTURE AND THE COSMOLOGICAL CONSTANT

2011 ◽  
Vol 03 ◽  
pp. 195-202
Author(s):  
M. D. MAIA
Keyword(s):  
Cosmological Constant ◽  
Riemannian Geometry ◽  
Extrinsic Curvature ◽  
Space Time ◽  
Local Change ◽  
Accelerated Expansion ◽  
Observable Effect ◽  
Cosmological Constant Problem ◽  
Expansion Of The Universe ◽  
The Universe

The concept of deformation of Riemannian geometry is reviewed, with applications to gravitation and cosmology. Starting with an analysis of the cosmological constant problem, it is shown that space-times are deformable in the sense of local change of shape. These deformations leave an observable signature in the space-time, characterized by a conserved tensor, associated with a tangent acceleration, defined by the extrinsic curvature of the space-time. In the applications to cosmology, we find that the accelerated expansion of the universe is the observable effect of the deformation, dispensing with the cosmological constant and its problems.

scholarly journals Cosmological constant from the emergent gravity perspective

2014 ◽  
Vol 23 (06) ◽  
pp. 1430011 ◽  
Author(s):  
T. Padmanabhan ◽  
Hamsa Padmanabhan
Keyword(s):  
Cosmological Constant ◽  
Sufficient Conditions ◽  
Integration Constant ◽  
Dimensionless Number ◽  
Late Time ◽  
Field Equations ◽  
Cosmological Constant Problem ◽  
Emergent Gravity ◽  
Background Material ◽  
The Universe

Observations indicate that our universe is characterized by a late-time accelerating phase, possibly driven by a cosmological constant Λ, with the dimensionless parameter [Formula: see text], where LP= (Għ/c3)1/2is the Planck length. In this review, we describe how the emergent gravity paradigm provides a new insight and a possible solution to the cosmological constant problem. After reviewing the necessary background material, we identify the necessary and sufficient conditions for solving the cosmological constant problem. We show that these conditions are naturally satisfied in the emergent gravity paradigm in which (i) the field equations of gravity are invariant under the addition of a constant to the matter Lagrangian and (ii) the cosmological constant appears as an integration constant in the solution. The numerical value of this integration constant can be related to another dimensionless number (called CosMIn) that counts the number of modes inside a Hubble volume that cross the Hubble radius during the radiation and the matter-dominated epochs of the universe. The emergent gravity paradigm suggests that CosMIn has the numerical value 4π, which, in turn, leads to the correct, observed value of the cosmological constant. Further, the emergent gravity paradigm provides an alternative perspective on cosmology and interprets the expansion of the universe itself as a quest towards holographic equipartition. We discuss the implications of this novel and alternate description of cosmology.

scholarly journals THE COSMOLOGICAL CONSTANT PROBLEM AND INFLATION IN THE STRING LANDSCAPE

2009 ◽  
Vol 24 (10) ◽  
pp. 1925-1962 ◽  
Author(s):  
QING-GUO HUANG ◽  
S.-H. HENRY TYE
Keyword(s):  
Cosmological Constant ◽  
Planck Scale ◽  
Brane World ◽  
Road Map ◽  
The Standard Model ◽  
Long Lifetime ◽  
String Landscape ◽  
Quantum Treatment ◽  
The Universe ◽  
Nucleation Bubble

An earlier paper points out that a quantum treatment of the string landscape is necessary. It suggests that the wave function of the universe is mobile in the landscape until the universe reaches a meta-stable site with its cosmological constant Λ0 smaller than the critical value Λc, where Λc is estimated to be exponentially small compared to the Planck scale. Since this site has an exponentially long lifetime, it may well be today's universe. We investigate specific scenarios based on this quantum diffusion property of the cosmic landscape and find a plausible scenario for the early universe. In the last fast tunneling to the Λ0(<Λc) site in this scenario, all energies are stored in the nucleation bubble walls, which are released to radiation only after bubble collisions and thermalization. So the Λ0 site is chosen even if Λ0 plus radiation is larger than Λc, as long as the radiation does not destabilize the Λ0 vacuum. A consequence is that inflation must happen before this last fast tunneling, so the inflationary scenario that emerges naturally is extended brane inflation, where the brane motion includes a combination of rolling, fast tunnelings, slow-roll, hopping and percolation in the landscape. We point out that, in the brane world, radiation during nucleosynthesis are mostly on the standard model branes (brane radiation, as opposed to radiation in the bulk). This distinction may lead to interesting dynamics. We consider this paper as a road map for future investigations.

scholarly journals The Solution to the Cosmological Constant Problem

2019 ◽  
Author(s):  
Brian Craig
Keyword(s):  
Cosmological Constant ◽  
Gamma Rays ◽  
Mass Density ◽  
Empty Space ◽  
Vacuum State ◽  
Cosmological Constant Problem ◽  
New Approach ◽  
Solid Crystal ◽  
Low Mass ◽  
The Universe

To account for the very low mass density associated with Dark Energy and the Cosmological Constant, a new approach to the ground state of empty space is presented. The resulting model for the vacuum state associated with empty space proposes a crystalline-like texture for the chromatic structure of empty space. This vacuum state has the appropriate mass density and predicts acceleration for the Universe expansion. Furthermore, the model predicts that this texture is anisotropic and may lead to measurable changes in the production of electron and positron pairs by gamma rays incident on a solid crystal of low mass density such as graphite.

scholarly journals Cold dark matter: Bose-Einstein condensation of gluons in Anti-de Sitter space time

2021 ◽  
Author(s):  
Gilles Cohen-Tannoudji ◽  
Jean-Pierre Gazeau
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Standard Model ◽  
Cosmological Constant ◽  
Cold Dark Matter ◽  
Hidden Variables ◽  
Einstein Condensation ◽  
De Sitter ◽  
Bose Einstein ◽  
The Universe

In the same way as the realization of some of the famous gedanken experiments imagined by the founding fathers of quantum mechanics has recently led to the current renewal of the interpretation of quantum physics, it seems that the most recent progresses of observational astrophysics can be interpreted as the realization of some cosmological gedanken experiments such as the removal from the universe of the whole visible matter or the cosmic time travel leading to a new cosmological standard model. This standard model involves two dark components of the universe, dark energy and dark matter. Whereas dark energy is usually associated with the positive cosmological constant, we propose to explain dark matter as a pure QCD effect. This effect is due to the trace anomaly viewed as a negative cosmological constant accompanying baryonic matter at the hadronization transition from the quark gluon plasma phase to the colorless hadronic phase. Our approach not only yields a ratio Dark/Visible equal to 11/2 but also provides gluons and (anti-)quarks with an extra mass of vibrational nature. Currently observed dark matter is thus interpreted as a gluon Bose Einstein condensate that is a relic of the quark period. Such an interpretation would comfort the idea that, apart from the violation of the matter/antimatter symmetry satisfying the Sakharov&rsquo;s conditions, the reconciliation of particle physics and cosmology needs not the recourse to any ad hoc fields, particles or hidden variables.

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