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Newtonian limit of Einstein equation with a cosmological constant

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Chinese Physics C 2024年第10期48卷 264-274页

作者： Li-Fang Li Zhoujian Cao Xiaokai He Institute of Mechanics Chinese Academy of SciencesBeijing 100190China Institute of Applied Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Fundamental Physics and Mathematical Sciences Hangzhou Institute for Advanced StudyUCASHangzhou 310024China School of Mathematics and Statistics Hunan First Normal UniversityChangsha 410205China

Traditionally,the cosmological constant has been viewed as dark energy that mimics matter with negative *** that matter with negative energy provides a repulsive force,which fundamentally differs from typical gravitational forces,it has been believed that the cosmological constant effectively contributes a repulsive ***,it is important to note that the concept of gravitational force is valid only within the framework of Newtonian *** this study,we demonstrate that the traditional understanding of the gravitational force contributed by the cosmological constant is not entirely *** approach involves investigating the Newtonian limit of the Einstein equation with a cosmological *** subtleties involved in this analysis are discussed in ***,we find that the effect of the cosmological constant on Newtonian gravity is an attractive force rather than a repulsive one for ordinary *** expected,this corrective force is negligibly ***,our findings may offer a way to distinguish between dark energy and the cosmological constant,as one contributes a repulsive force while the other contributes an attractive force.

关键词： cosmological constant dark matter Einstein equation Newtonian limit dark energy

cosmological constant and Energy Density of Random Electromagnetic Field

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Journal of High Energy Physics, Gravitation and Cosmology 2016年第3期2卷 312-319页

作者： Ilya A. Obukhov Research & Development Company “System Recourses” Moscow Russia

It is shown that the non-equilibrium electrically neutral and relativistically invariant vacuum-like state with the negative energy density and positive pressure may exist at the non-zero temperature in the system of spinor particles, antiparticles, and random electromagnetic field generated by particle-particle, particle-antiparticle, and antiparticle-antiparticle transitions. At the temperature of the order of 10 -5 K, the energy density of its state corresponds to the dark energy density in absolute magnitude. The cosmological constant for such material medium turns out to be negative.

关键词： Dark Energy cosmological constant Stochastic Electromagnetic Field Spinor Particles

A Solution to the cosmological constant Problem Using the Holographic Principle (A Brief Note)

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Journal of Modern Physics 2024年第2期15卷 159-166页

作者： Eugene Terry Tatum Independent Researcher Bowling Green Kentucky USA

This paper integrates a quantum conception of the Planck epoch early universe with FSC model formulae and the holographic principle, to offer a reasonable explanation and solution of the cosmological constant problem. Such a solution does not appear to be achievable in cosmological models which do not integrate black hole formulae with quantum formulae such as the Stephan-Boltzmann law. As demonstrated herein, assuming a constant value of Lambda over the great span of cosmic time appears to have been a mistake. It appears that Einstein’s assumption of a constant, in terms of vacuum energy density, was not only a mistake for a statically-balanced universe, but also a mistake for a dynamically-expanding universe.

关键词： Quantum Cosmology Planck Scale cosmological constant Black Holes Holographic Principle Flat Space Cosmology AdS-CFT ER = EPR Cosmology Model

A Solution of the cosmological constant and DE and Arrow of Time, Using Model of a Nonsingular Universe from Rosen from Volume (56) Ettore Majorana International Science Series, Physics, 1991

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Journal of High Energy Physics, Gravitation and Cosmology 2021年第3期7卷 925-935页

作者： Andrew Beckwith Physics Department College of Physics Chongqing University Chongqing China

We reduplicate the Book “Dark Energy” by M. Li, X-D. Li, and Y. Wang, given zero-point energy calculation with an unexpected “length” added to the “width” of a graviton wave just prior to specifying the creation of “gravitons”, using the Rosen and Israelit model of a nonsingular universe. In doing so we are in addition to obtaining a wavelength 1030 times greater than Planck’s length so we can calculate DE, may be able to with the help of the Rosen and Israelit model have a first approximation as to the arrow of time, and a universe with massive gravity. We have left the particulars of the nonsingular starting point undefined but state that the Rosen and Israelit model postulates initial temperatures of 10-180 Kelvin and also a value of about Planck temperature, at 10-3 centimeters radii value which may satisfy initial conditions asked by t’Hooft for describing an arrow of time. A key assumption is that the DE is formed at 10-3 cm, after an expansion of 1030 times in radii, from the Planck length radius nonsingular starting point. The given starting point for DE in this set of assumptions is where there is a change in the cosmic acceleration, to a zero value, according to Rosen and Israel, with time t = 1.31 times 10-42 seconds. That may be where we may specify a potential magnitude, V, which has ties into inflaton physics. The particulars of the model from Rosen and Israelit allow a solution to be found, without discussion of where that nonsingular starting point came from, a point the author found in need of drastic remedies and fixes.

关键词： Minimum Scale Factor cosmological constant Space-Time Bubble DE Arrow of Time

Mass of the Universe from Quarks: A Plausible Solution to the cosmological constant Problem

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Journal of Modern Physics 2023年第12期14卷 1672-1692页

作者： Kevin Oramah Department of Mathematics and Physics University of Stavanger Stavanger Norway

A framework to estimate the mass of the universe from quarks is presented, taking spacetime into account. This is a link currently missing in our understanding of physics/science. The focus on mass-energy balance is aimed at finding a solution to the cosmological constant (CC) problem by attempting to quantize space-time and linking the vacuum energy density at the beginning of the universe and the current energy density. The CC problem is the famous disagreement of approximately 120 orders of magnitude between the theoretical energy density at the Planck scale and the indirectly measured cosmological energy density. Same framework is also used to determine the mass of the proton and neutron from first principles. The only input is the up quark (u-quark) mass, or precisely, the 1st generation quarks. The method assumes that the u-quark is twice as massive as the down-quark (d-quark). The gap equation is the starting point, introduced in its simplest form. The main idea is to assume that all the particles and fields in the unit universe are divided into quarks and everything else. Everything else means all fields and forces present in the universe. It is assumed that everything else can be “quark-quantized”;that is, assume that they can be quantized into similar sizeable u-quarks and/or it’s associated interactions and relations. The result is surprisingly almost as measured and known values. The proton structure and mass composition are also analysed, showing that it likely has more than 3 quarks and more than 3 valence quarks. It is also possible to estimate the percentage of dark matter, dark energy, ordinary matter, and anti-matter. Finally, the cosmological constant problem or puzzle is resolved by connecting the vacuum energy density of Quantum Field Theory (5.1E+96 kg/m3) and the energy density of General Relativity (1.04E−26 kg/m3). Upon maturation, this framework can serve as a bridging platform between Quantum Field Theory and General

关键词： cosmological constant Proton Mass-Structure Quark-Quantization Dark Matter Dark Energy Age of the Universe Energy Density Spacetime Quantization

How to Use Starobinsky Inflationary Potential Plus Argument from Alder, Bazin, and Schiffer as Radial Acceleration to Obtain First Order Approximation as to Where/When cosmological constant May Form

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Journal of High Energy Physics, Gravitation and Cosmology 2022年第4期8卷 1012-1018页

作者： Andrew Walcott Beckwith Physics Department Chongqing University Chongqing China

Using the Klauder enhanced quantization as a way to specify the cosmological constant as a baseline for the mass of a graviton, we eventually come up and then we will go to the Starobinsky potential as a replacement for the term N used in Equation (3) and Equation (4). From there we will read in a way to describe conditions allowing for where the cosmological constant may be set. The idea also is to describe a regime of space-time where the initial perturbation/start to inflation actually occurred, as is alluded to in the final part of the document.

关键词： Radial Acceleration cosmological constant Raviton

A NEW CLASS OF SOLUTIONS OF VACUUM EINSTEIN'S FIELD EQUATIONS WITH cosmological constant

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Annals of Applied Mathematics 2016年第1期32卷 36-41页

作者： Ming Shen Qiaorong Zhuang College of Math.and Computer Science Fuzhou University

In this paper, a new class of solutions of the vacuum Einstein＇s field equa- tions with cosmological constant is obtained. This class of solutions possesses the naked physical singularity. The norm of the Riemann curvature tensor of this class of solutions takes infinity at some points and the solutions do not have any event horizon around the singularity.

关键词： vacuum Einstein's field equations cosmological constant ex-act solutions naked physical singularity

How the Narlikar Argument of Quantum Gravity Can Be Combined with the cosmological constant We Calculated to Obtain Quantum Gravity Effects for Plank Length Values, as Opposed to 2 Times Planck Length Values

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Journal of High Energy Physics, Gravitation and Cosmology 2021年第2期7卷 445-451页

作者： Andrew Beckwith Physics Department Chongqing University Huxi Campus Chongqing China

We take the results where we reduplicate the Book “Dark Energy” by M. Li, X-D. Li, and Y. Wang, zero-point energy calculation, as folded in with the Klauder methodology, as given in a prior publication. From there we first access the Rosen solution to a mini universe energy to ascertain an energy value of t, the pre-inflationary near singularity, then access what would be needed as to inject information into our universe. We then close with an argument by Narilkar as to a quantum bound on the Einstein-Hilbert action integral, so as to obtain quantum Gravity. Narlikar omits the cosmological constant. We keep it in, for our overall conclusion about the cosmological constant and its relevance to Quantum gravity.

关键词： Minimum Scale Factor cosmological constant Space-Time Bubble Bouncing Cosmologies

Entropy and cosmological constant of a Universe Calculated by Means of Dimensional Analysis, Margolus-Levitin Theorem and Landauer’s Principle

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Journal of Modern Physics 2023年第10期14卷 1310-1322页

作者： Mario Leo Dipartimento di Matematica e Fisica ‘‘Ennio De Giorgi’’ Università del Salento Lecce Italy

By means of the dimensional analysis a spherically simmetric universe with a mass M = c3/(2HG) and radius equal to c/H is considered, where H is the Hubble constant, c the speed of light and G the Newton gravitational constant. The density corresponding to this mass is equal to the critical density ρcr = 3H2/(8πG). This universe evolves according to a Bondi-Gold-Hoyle scenario, with continuous creation of matter at a rate such to maintain, during the expansion, the density always critical density. Using the Margolus-Levitin theorem and the Landauer’s principle, an entropy is associated with this universe, obtaining a formula having the same structure as the Bekenstein-Hawking formula of the entropy of a black hole. Furthermore, a time-dependent cosmological constant Λ, function of the Hubble constant and the speed of light, is proposed.

关键词： cosmological Models cosmological constant Entropy