scholarly journals The Higgs field and the resolution of the Cosmological Constant Paradox in the Weyl-geometrical Universe

2017 ◽  
Vol 375 (2106) ◽  
pp. 20160388 ◽  
Author(s):  
Francesco De Martini
Keyword(s):  
Differential Geometry ◽  
Dark Energy ◽  
Cosmological Constant ◽  
Energy Content ◽  
Critical Density ◽  
Space Time ◽  
Universal Theory ◽  
Electroweak Theory ◽  
Parallel Displacement ◽  
The Universe

The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of Weyl's differential geometry: the parallel displacement of vectors in curved space–time. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the SU (2) L ⊗ U (1) Y as well as on the conformal groups of space–time Weyl's transformations is analysed within the framework of a general-relativistic, conformally covariant scalar-tensor theory that includes the electromagnetic and the Yang–Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An ‘effective cosmological potential’: V eff is expressed in terms of the dark energy potential: via the ‘mass reduction parameter’: , a general property of the Universe. The mass of the Higgs boson, which is considered a ‘free parameter’ by the standard electroweak theory, by our theory is found to be proportional to the mass which accounts for the measured cosmological constant, i.e. the measured content of vacuum-energy in the Universe. The non-integrable application of Weyl's geometry leads to a Proca equation accounting for the dynamics of a ϕ ρ -particle, a vector-meson proposed as an an optimum candidate for dark matter. On the basis of previous cosmic microwave background results our theory leads, in the condition of cosmological ‘critical density’, to the assessment of the average energy content of the ϕ ρ -excitation. The peculiar mathematical structure of V eff offers a clue towards a very general resolution of a most intriguing puzzle of modern quantum field theory, the ‘Cosmological Constant Paradox’ (here referred to as the ‘ Λ -Paradox’). Indeed, our ‘universal’ theory offers a resolution of the Λ -Paradox for all exponential inflationary potentials: V Λ ( T , ϕ )∝ e − nϕ , and for all linear superpositions of these potentials, where n belongs to the mathematical set of the ‘real numbers’. An explicit solution of the Λ -Paradox is reported for n =2. The resolution of the Λ -Paradox cannot be achieved in the context of Riemann's differential geometry. This article is part of the themed issue ‘Second quantum revolution: foundational questions’.

The quantum Higgs field and the resolution of the cosmological constant paradox in the Weyl-geometrical Universe

2017 ◽  
Vol 15 (08) ◽  
pp. 1740025
Author(s):  
Francesco De Martini
Keyword(s):  
Dark Energy ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Vacuum Energy Density ◽  
Universal Theory ◽  
Recent Experimental Data ◽  
Electroweak Theory ◽  
Mass Reduction ◽  
Parallel Displacement ◽  
The Universe

The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of the Weyl’s differential geometry: the parallel displacement of vectors in curved spacetime. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the [Formula: see text] as well as on the conformal groups of spacetime Weyl’s transformations is analyzed within the framework of a general-relativistic, conformally-covariant scalar–tensor theory that includes the electromagnetic and the Yang–Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An “effective cosmological potential”: [Formula: see text] is expressed in terms of the dark energy potential: [Formula: see text] via the “mass reduction parameter”: [Formula: see text], a general property of the Universe. The mass of the Higgs boson, which is considered a “free parameter” by the standard electroweak theory, by our theory is found to be proportional to the mass [Formula: see text] which contributes to the measured Cosmological Constant, i.e. the measured content of vacuum-energy in the Universe. The nonintegrable application of the Weyl’s geometry leads to a Proca equation accounting for the dynamics of a [Formula: see text]-particle, a vector-meson proposed as an optimum candidate for Dark Matter. The peculiar mathematical structure of [Formula: see text] offers a clue towards a very general resolution in 4-D of a most intriguing puzzle of modern quantum field theory, the “cosmological constant paradox”(here referred to as: “[Formula: see text]-paradox”). Indeed, our “universal” theory offers a resolution of the “[Formula: see text]-paradox” for all exponential inflationary potentials: [Formula: see text], and for all linear superpositions of these potentials, where [Formula: see text] belongs to the mathematical set of the “real numbers”. An explicit solution of the [Formula: see text]-Paradox is reported for [Formula: see text]. The results of the theory are analyzed in the framework of the recent experimental data of the PLANCK Mission. The average vacuum-energy density in the Universe is found: [Formula: see text], the mass-reduction parameter: [Formula: see text] and the value of the “cosmological constant”: [Formula: see text](eV/c[Formula: see text]. A quite remarkable result of the theory consists of the complete formulation of the Einstein equation including in its structure the “cosmological constant”, [Formula: see text]. This was the term that Einstein added “by hand” to his famous equation. The critical stability of the Universe is also discussed.

Nonvibrating energy strings as fundamental building blocks of space and particles

2019 ◽  
Vol 32 (3) ◽  
pp. 338-352
Author(s):  
Albert Zur (Albo)
Keyword(s):  
Dark Energy ◽  
Cosmological Constant ◽  
Displacement Vector ◽  
Building Blocks ◽  
Space Time ◽  
Accelerated Expansion ◽  
Absolute Space ◽  
Position Space ◽  
3D Space ◽  
The Universe

In the proposed Energy String (ES) theory, we assume the existence of fundamental energy strings forming a generally Euclidean four-dimensional fabric of empty space as well as forming all types of particles in the universe. The 4D space fabric is composed of space energy strings bearing dark-energy as well as a newly described dark-momentum. Particles are composed of particle energy strings which interact with space energy strings inducing three-dimensional space curvatures embedded in a flat fourth-space dimension. The induced space curvatures are responsible for gravity of particles and assign a longitudinal and a transverse direction to particles. The proposed ES theory yields an adapted model of the universe with remarkable teachings as follows: (1) The fabric of space and related dark-energy are associated with a newly defined dark-momentum. This dark momentum is the sole contributor to the cosmological constant Λ in Einstein's field equations which describes the accelerated expansion of the universe. The energy of the quantum vacuum becomes nonrelevant to the cosmological constant Λ, enabling a solution to the “Cosmological Constant Problem”; (2) All particles perform an equal distance of translatory displacement in 4D-space, reflecting a universal displacement rate of particles relative to an absolute generally Euclidean 4D-space. This universal principle is equivalent to Lorentz transformation of a fundamental four-displacement vector, representing a new model of Special Relativity with superior compatibility to quantum theories. (3) Time is a displacement property of mass particles in 4D-space. Frames of 3D-space+time are the perspective by which mass particles experience 4D-space. In this perspective, absolute space longitudinally displaces over mass particles experienced as proper time elapse. Temporal momentum is an inherent invariant property of mass particles. Frames of 3D-space+time are mixed domains: three spatial coordinates of position-space and a temporal coordinate of momentum-space, meaning the position-space in the temporal coordinate is totally inaccessible.

scholarly journals Dark Energy and Cosmological Constant

2018 ◽  
Vol 17 (1) ◽  
pp. 25-32
Author(s):  
Louise Rebecca ◽  
C Sivaram ◽  
Kenath Arun
Keyword(s):  
Dark Energy ◽  
Cosmological Constant ◽  
Mass Density ◽  
Critical Density ◽  
Accelerated Expansion ◽  
Microwave Background ◽  
Type Ia ◽  
Expansion Of The Universe ◽  
Ia Supernovae ◽  
The Universe

One of the unresolved problems in cosmology is that the measured mass density of the universe has revealed a value that was about 30% of the critical density. Since the universe is very nearly spatially flat, as is indicated by measurements of the cosmic microwave background, about 70% of the energy density of the universe was left unaccounted for. Another observation seems to be connected to this mystery. Generally one would expect the rate of expansion to slow down once the universe started expanding. The measurements of Type Ia supernovae have revealed that the expansion of the universe is actually accelerating. This accelerated expansion is attributed to the so-called dark energy (DE).Here we give a brief overview on the observational basis for DE hypothesis and how cosmological constant, initially proposed by Einstein to obtain a static universe, can play the role of dark energy.

scholarly journals Expansion of the universe and its correlation with dark energy

2020 ◽  
Vol 8 (1) ◽  
pp. 10
Author(s):  
Puja Tiwari ◽  
Prof . M.N Bandyopadhyay ◽  
Satakshi Chatterjee ◽  
Prof. S. N. Bandyopadhyay
Keyword(s):  
Dark Energy ◽  
Cosmological Constant ◽  
Gravitational Force ◽  
Big Bang ◽  
Space Time ◽  
Red Shift ◽  
Expansion Of The Universe ◽  
The Big Bang ◽  
The Relationship ◽  
The Universe

The Universe is expanding and science has got the relevant amount of evidence to prove that. The red shift of the distant galaxies prove that the Universe is expanding and at a good rate. The trouble is not with the expansion rather the force that is helping in this expansion. The Four Forces that is understood by physics are Gravitational Force, Electromagnetic Force, The Weak Force and The Strong Force. The four forces mentioned above unfortunately does not help in understanding the expansion of the Universe even after 13.8 billion years from the Big Bang. Initially it was thought that the Universe had an exponential expansion just after the Big Bang and this expansion will slow down before Gravity starts contracting the Universe. Well this theory got a setback after the Red Shift of the Galaxies showed that the Universe is still expanding.The expansion is happening still which means that the Gravitational Force is not being able to drift the galaxies towards one another. So what could be the unknown force that is repelling the galaxies from one another? Scientists have been working on this issue and many new concepts have been developed. Many scientists have argued that there is some force that is repelling the Universe but understanding this force has been difficult till now. Major scientists now agree that there is a force that is repelling the Universe and this force is not the four fundamental forces that are known to us. They have termed this force as the Dark Energy.What is this Dark Energy is a haunting question in today’s world. Only around 5% of the observable Universe is known till date. The rest around 95% is still a mystery to us. Of that 95% around 68% is Dark Energy. So the importance of understanding this force is the need of the hour. This force can tell a lot about the formation of the Universe from the start or it can even enlighten us if the Universe is eternal.The issue is as of now, this Dark Energy is hypothetical in nature as it has not been seen or felt by the instruments available to science today. The idea of Dark Energy goes to explain the expansion of the Universe, if Dark Energy is taken as some sort of Anti- Gravitational Force.Einstein’s theory of relativity talks of how space and time is intermingled with gravity. According to this theory space time gets modified due to the amount of matter that falls into the space. So if a planet sits on a space in the Universe it will cause a deviation in the space time field in such a way that it will accommodate the matter of the planet. So Einstein placed time as the fourth dimension and showed its importance in space. This theory stands true in majority of the cases in the Universe. The only hurdle being that inside the Black Hole this theory falters.Einstein and Schrodinger did interact with one another after he had understood that the Universe was expanding through the theory presented by Hubble. Earlier Einstein had stated that the Universe was Static. To counter the exigency that space time changes with matter he had proposed a constant by the name Cosmological Constant. Later he took the constant away stating that it was his blunder not to understand that the Universe was Expanding. Schrodinger had proposed to put the Cosmological Constant in the right side of the equation. This meant the constant may change with time and be considered more of a variable force. Though, Einstein later did not agree to the idea. Still it can be considered that both of them were talking about an extra force but could not come to any conclusion on this.Einstein in his special relativity theory had talked of conversion of energy to matter with his famous equation, E=mc^2. This meant that energy can be formed by matter and matter can be converted into energy. Though energy created from matter can be seen in Atom Bomb but matter created from energy is not seen. This paper will try to show how matter can be created from energy where Dark Energy acts as a Catalyst.This paper also tries to analyze the concept of Dark Energy as a non interacting supermassive energy (NISE). The paper will try to see the relationship between expanding Universe and Dark energy. The paper will try to develop a new spectrum that can make Dark Energy or NISE as stated in the paper visible or understandable. The paper will also like to see the relationship between Dark Energy and Photon. The paper will try to show how energy is converted from matter with the help of Dark Energy. 

Cosmological constant

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Dark Energy ◽  
Cosmological Constant ◽  
Accelerated Expansion ◽  
Vacuum Fluctuations ◽  
Present Epoch ◽  
Modify Gravity ◽  
Expansion Of The Universe ◽  
The Universe

The contribution of vacuum fluctuations to the cosmological constant is reconsidered studying the dependence on the used regularisation scheme. Then alternative explanations for the observed accelerated expansion of the universe in the present epoch are introduced which either modify gravity or add a new component of matter, dubbed dark energy. The chapter closes with some comments on attempts to quantise gravity.

scholarly journals ANISOTROPIC COMPACT STARS WITH VARIABLE COSMOLOGICAL CONSTANT

2012 ◽  
Vol 21 (13) ◽  
pp. 1250088 ◽  
Author(s):  
SK. MONOWAR HOSSEIN ◽  
FAROOK RAHAMAN ◽  
JAYANTA NASKAR ◽  
MEHEDI KALAM ◽  
SAIBAL RAY
Keyword(s):  
Dark Energy ◽  
Cosmological Constant ◽  
Compact Star ◽  
Compact Stars ◽  
Radial Dependence ◽  
Regularity Conditions ◽  
Variable Cosmological Constant ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Surface Redshift

Recently, the small value of the cosmological constant and its ability to accelerate the expansion of the universe is of great interest. We discuss the possibility of forming of anisotropic compact stars from this cosmological constant as one of the competent candidates of dark energy. For this purpose, we consider the analytical solution of Krori and Barua metric. We take the radial dependence of cosmological constant and check all the regularity conditions, TOV equations, stability and surface redshift of the compact stars. It has been shown as conclusion that this model is valid for any compact star and we have cited 4U 1820-30 as a specific example of that kind of star.

scholarly journals WHY THERE IS SOMETHING SO CLOSE TO NOTHING: TOWARDS A FUNDAMENTAL THEORY OF THE COSMOLOGICAL CONSTANT

2007 ◽  
Vol 22 (10) ◽  
pp. 1797-1818 ◽  
Author(s):  
VISHNU JEJJALA ◽  
DJORDJE MINIC
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Uncertainty Relation ◽  
Space Time ◽  
Large Size ◽  
Minkowski Space Time ◽  
The Universe ◽  
Canonical Quantum

The cosmological constant problem is turned around to argue for a new foundational physics postulate underlying a consistent quantum theory of gravity and matter, such as string theory. This postulate is a quantum equivalence principle which demands a consistent gauging of the geometric structure of canonical quantum theory. We argue that string theory can be formulated to accommodate such a principle, and that in such a theory the observed cosmological constant is a fluctuation about a zero value. This fluctuation arises from an uncertainty relation involving the cosmological constant and the effective volume of space–time. The measured, small vacuum energy is dynamically tied to the large "size" of the universe, thus violating naive decoupling between small and large scales. The numerical value is related to the scale of cosmological supersymmetry breaking, supersymmetry being needed for a nonperturbative stability of local Minkowski space–time regions in the classical regime.

scholarly journals Generalized Phenomenological Models of Dark Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Prasenjit Paul ◽  
Rikpratik Sengupta
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Energy Density ◽  
Cosmological Constant ◽  
Phenomenological Models ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Free Parameters ◽  
The Universe ◽  
Matter Energy

It was first observed at the end of the last century that the universe is presently accelerating. Ever since, there have been several attempts to explain this observation theoretically. There are two possible approaches. The more conventional one is to modify the matter part of the Einstein field equations, and the second one is to modify the geometry part. We shall consider two phenomenological models based on the former, more conventional approach within the context of general relativity. The phenomenological models in this paper consider a Λ term firstly a function of a¨/a and secondly a function of ρ, where a and ρ are the scale factor and matter energy density, respectively. Constraining the free parameters of the models with the latest observational data gives satisfactory values of parameters as considered by us initially. Without any field theoretic interpretation, we explain the recent observations with a dynamical cosmological constant.

scholarly journals ACCELERATION AND DECELERATION IN THE CURVATURE-INDUCED PHANTOM MODEL OF THE LATE AND FUTURE UNIVERSE: COSMIC COLLAPSE AND ITS QUANTUM ESCAPE

2009 ◽  
Vol 18 (05) ◽  
pp. 865-887
Author(s):  
S. K. SRIVASTAVA ◽  
J. DUTTA
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Early Universe ◽  
High Energy ◽  
High Energy Density ◽  
Energy Models ◽  
Acceleration And Deceleration ◽  
The Universe

In this paper, the cosmology of the late and future universe is obtained from f(R) gravity with nonlinear curvature terms R2 and R3 (R is the Ricci scalar curvature). It is different from f(R) dark energy models where nonlinear curvature terms are taken as a gravitational alternative to dark energy. In the present model, neither linear nor nonlinear curvature terms are taken as dark energy. Rather, dark energy terms are induced by curvature terms and appear in the Friedmann equation derived from f(R) gravitational equations. This approach has an advantage over f(R) dark energy models in three ways: (i) results are consistent with WMAP observations, (ii) dark matter is produced from the gravitational sector and (iii) the universe expands as ~ t2/3 during dominance of the curvature-induced dark matter, which is consistent with the standard cosmology. Curvature-induced dark energy mimics phantom and causes late acceleration. It is found that transition from matter-driven deceleration to acceleration takes place at the redshift 0.36 at time 0.59 t0 (t0 is the present age of the universe). Different phases of this model, including acceleration and deceleration during the phantom phase, are investigated. It is found that expansion of the universe will stop at the age of 3.87 t0 + 694.4 kyr. After this epoch, the universe will contract and collapse by the time of 336.87 t0 + 694.4 kyr. Further, it is shown that cosmic collapse obtained from classical mechanics can be avoided by making quantum gravity corrections relevant near the collapse time due to extremely high energy density and large curvature analogous to the state of the very early universe. Interestingly, the cosmological constant is also induced here; it is extremely small in the classical domain but becomes very high in the quantum domain. This result explains the largeness of the cosmological constant in the early universe due to quantum gravity effects during this era and its very low value in the present universe due to negligible quantum effect in the late universe.

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.

Sign in / Sign up

Export Citation Format

Share Document