Search

In this paper, we make use of the generalized zeta function technique to investigate the vacuum energy, temperature corrections and heat kernel coefficients associated with a scalar field under a quasiperiodic condition in a (D + 1) -dimensional conical spacetime. In this scenario, we find that the renormalized vacuum energy, as well as the temperature corrections, are both zero. The nonzero heat kernel coefficients are the ones related to the usual Euclidean divergence, and also to the nontrivial aspects of the quaisperiodically identified conical spacetime topology. An interesting result that arises in this configuration is that for some values of the quasiperiodic parameter, the heat kernel coefficient associated with the nontrivial topology vanishes. In addition, we also consider the scalar field in a (D + 1) -dimensional spacetime formed by the combination of a conical and screw dislocation topological defects. In this case, we obtain a nonzero renormalized vacuum energy density and its corresponding temperature corrections. Again, the nonzero heat kernel coefficients found are the ones related to the Euclidean and nontrivial topology divergences. For D = 3 , we explicitly show, in the massless scalar field case, the limits of low and high temperatures for the free energy. In the latter, we show that the free energy presents a classical contribution. [ABSTRACT FROM AUTHOR]

In this paper, we calculate the vacuum energy as a functional from the phion propagator in 4D model of complex scalar field (phion) which interacts with a real matrix scalar field (chion). The condition of stationarity of this functional gives us the equation for phion propagator. At some critical value of the coupling, the propagator changes its asymptotic behavior in the deep-Euclidean region of momenta. This behavior corresponds to some critical phenomenon. The study of the convexity of the energy functional shows that the solution obtained actually corresponds to the theory. We also discuss the stabilization of the ground state in the strong-coupling region by effective self-action of phions. [ABSTRACT FROM AUTHOR]

We explore the dependence of vacuum energy on the boundary conditions for massive scalar fields in (2 + 1)-dimensional spacetimes. We consider the simplest geometrical setup given by a two-dimensional space bounded by two homogeneous parallel wires in order to compare it with the non-perturbative behaviour of the Casimir energy for non-Abelian gauge theories in (2 + 1) dimensions. Our results show the existence of two types of boundary conditions which give rise to two different asymptotic exponential decay regimes of the Casimir energy at large distances. The two families are distinguished by the feature that the boundary conditions involve or not interrelations between the behaviour of the fields at the two boundaries. Non-perturbative numerical simulations and analytical arguments show such an exponential decay for Dirichlet boundary conditions of SU(2) gauge theories. The verification that this behaviour is modified for other types of boundary conditions requires further numerical work. Subdominant corrections in the low-temperature regime are very relevant for numerical simulations, and they are also analysed in this paper. [ABSTRACT FROM AUTHOR]

I consider the electro-weak (EW) masses and interactions generated by photons using vacuum expectation values of Stueckelberg and Higgs fields. I provide a prescription to relate their parametric values to a cosmological range derived from the fundamental Heisenberg uncertainty principle and the Einstein–de Sitter cosmological constant and horizon. This yields qualitative connections between microscopic ranges acquired by W ± or Z 0 gauge Bosons and the cosmological scale and minimal mass acquired by g-photons. I apply this procedure to an established Stueckelberg–Higgs mechanism, while I consider a similar procedure for a pair of Higgs fields that may spontaneously break all U(1) × SU(2) gauge invariances. My estimates of photon masses and their additional parity-breaking interactions with leptons and neutrinos may be detectable in suitable accelerator experiments. Their effects may also be observable astronomically through massive g-photon condensates that may contribute to dark matter and dark energy. [ABSTRACT FROM AUTHOR]

We explore the dependence of vacuum energy on the boundary conditions for massive scalar fields in (2 + 1)-dimensional spacetimes. We consider the simplest geometrical setup given by a two-dimensional space bounded by two homogeneous parallel wires in order to compare it with the non-perturbative behaviour of the Casimir energy for non-Abelian gauge theories in (2 + 1) dimensions. Our results show the existence of two types of boundary conditions which give rise to two different asymptotic exponential decay regimes of the Casimir energy at large distances. The two families are distinguished by the feature that the boundary conditions involve or not interrelations between the behaviour of the fields at the two boundaries. Non-perturbative numerical simulations and analytical arguments show such an exponential decay for Dirichlet boundary conditions of SU(2) gauge theories. The verification that this behaviour is modified for other types of boundary conditions requires further numerical work. Subdominant corrections in the low-temperature regime are very relevant for numerical simulations, and they are also analysed in this paper.

I consider the electro-weak (EW) masses and interactions generated by photons using vacuum expectation values of Stueckelberg and Higgs fields. I provide a prescription to relate their parametric values to a cosmological range derived from the fundamental Heisenberg uncertainty principle and the Einstein–de Sitter cosmological constant and horizon. This yields qualitative connections between microscopic ranges acquired by W± or Z0 gauge Bosons and the cosmological scale and minimal mass acquired by g-photons. I apply this procedure to an established Stueckelberg–Higgs mechanism, while I consider a similar procedure for a pair of Higgs fields that may spontaneously break all U(1) × SU(2) gauge invariances. My estimates of photon masses and their additional parity-breaking interactions with leptons and neutrinos may be detectable in suitable accelerator experiments. Their effects may also be observable astronomically through massive g-photon condensates that may contribute to dark matter and dark energy.

The possibility that the vacuum energy density (VED) ρ vac could be time dependent in the expanding Universe is intuitively more reasonable than just a rigid cosmological constant for the entire cosmic history. The dynamics of ρ vac = ρ vac (H) as a function of the Hubble rate, H (t) , most likely contributes to alleviate cosmological problems and tensions, having also implications on the so-called fundamental 'constants' of Nature, which should be slowly drifting with the cosmic expansion owing to the fluctuations of the quantum vacuum. This includes the gravitational 'constant' G, but also the gauge and Yukawa couplings as well as the particle masses themselves (both of dark matter and baryonic matter). The subtle exchange of energy involved is the basis for the "micro and macro connection". Herein, I discuss not only this connection as a possibility but also show that it is in fact a generic prediction of QFT in cosmological spacetime which is fully compatible with general covariance. This fact has not been pointed out until recently when an appropriate renormalization framework for the VED has been found which is free from the usual conundrums associated with the cosmological constant problem. [ABSTRACT FROM AUTHOR]

We investigate the qualitative cosmic dynamics of varying vacuum models with the non-flat, homogeneous and isotropic background. In these models, the dark matter interacts with the vacuum energy. We utilize the dynamical system technique to explore the existence and stability of fixed points. The existence of radiation and matter dominated decelerating phase of the universe may be explained in these models. The accelerating universe expansion may also be explained due to the existence of an attractor in these models. Further, the numerical solution technique is incorporated to solve the autonomous systems. These solutions are utilized to illustrate the evolution of cosmographic and statefinder parameters along with the energy conditions. The Milne universe solution exists in the model which is a consequence of spatially curved geometry. The stability criterion of the fixed points reveals that the cosmic history in the considered models may be observationally viable. Furthermore, the strength of interaction terms are constrained using the observational estimates of the cosmographic parameters. [ABSTRACT FROM AUTHOR]

This talk summarizes a new understanding of the cosmological constant problem, which essentially relies on a phase-space-like computation of the vacuum energy, both in the realm of quantum field theory coupled to gravity, and in the realm of a consistent formulation of a quantum theory of gravity and matter, such as string theory, combined with central properties of gravitational entropy as captured by the Bekenstein bound. This new understanding of the vacuum in a quantum theory of gravity and matter sheds light on the Higgs mass as well as the masses of quarks and leptons. [ABSTRACT FROM AUTHOR]

For QFT on a lattice of dimension , the vacuum energy (both bosonic and fermionic) is zero if the Hamiltonian is a function of the square of the momentum, and the calculation of the vacuum energy is performed in the ring of residue classes modulo . This fact is related to a problem from number theory about the number of ways to represent a number as a sum of squares in the ring of residue classes modulo . [ABSTRACT FROM AUTHOR]

Introduction/purpose: Quantum field theory techniques are able to describe precisely, inter alia, collective phenomena of statistical and solid state physics. Method: The path integral method with a Wick rotation shows its complete analogy with the partition function of statistical mechanics. Results: The Landau-Ginzburg phenomenology successfully describes collective phenomena such as spontaneous magnetization and super-conductivity. Conclusions: Symmetry breaking phenomena could give macroscopic results.

Introduction/purpose: The quantization of the electromagnetic field gives rise to quantum fluctuations which in turn produce a force on macroscopic boundaries. This phenomenon is called the Casimir effect. Method: The second quantization of the electromagnetic field is employed. The Zeta function regularization technique has been applied. Results: Because of the electromagnetic field quantization, a force on macroscopic boundaries is observed. Conclusions: Vacuum fluctuations due to quantum effects give macroscopic results.

The present review aims to show that a modified space–time with an invariant minimum speed provides a relation with Weyl geometry in the Newtonian approximation of weak-field. The deformed Special Relativity so-called Symmetrical Special Relativity (SSR) has an invariant minimum speed V, which is associated with a preferred reference frame SV for representing the vacuum energy, thus leading to the cosmological constant (Λ). The equation of state (EOS) of vacuum energy for Λ, i.e., ρΛ=ϵ=−p emerges naturally from such space–time, where p is the pressure and ρΛ=ϵ is the vacuum energy density. With the aim of establishing a relationship between V and Λ in the modified metric of the space–time, we should consider a dark spherical universe with Hubble radius RH, having a very low value of ϵ that governs the accelerated expansion of universe. In doing this, we aim to show that SSR-metric has an equivalence with a de-Sitter (dS)-metric (Λ>0). On the other hand, according to the Boomerang experiment that reveals a slightly accelerated expansion of the universe, SSR leads to a dS-metric with an approximation for Λ<

Introduction/purpose: Quantum field theory techniques are able to describe precisely, inter alia, collective phenomena of statistical and solid state physics. Method: The path integral method with a Wick rotation shows its complete analogy with the partition function of statistical mechanics. Results: The Landau–Ginzburg phenomenology successfully describes collective phenomena such as spontaneous magnetization and superconductivity. Conclusions: Symmetry breaking phenomena could give macroscopic results. [ABSTRACT FROM AUTHOR]

Analytical modeling presents symmetries and aesthetic-mathematical characteristics which are not catchable in numerical computation for science and technology; nanoscience plays a significant role in unification attempts, considering also models including holistic aspects of reality. In this paper we present new discovered results about the complete analytical quantum-relativistic form of the mean square deviation of position R 2 (t) related to a recently introduced Drude–Lorentz-like model (DS model), already performed at classical, quantum and relativistic level. The function R 2 (t) gives precise information about the distance crossed by carriers (electrons, ions, etc.) inside a nanostructure, considering both quantum effects and relativistic velocities. The model has a wide scale range of applicability; the nanoscale is considered in this paper, but it holds application from sub-pico-level to macro-level because of the existence of a gauge factor, making it applicable to every oscillating process in nature. Examples of application and suggestions supplement this paper, as well as interesting developments to be studied related to the model and to one of the basic elements of a current unified holistic approach based on vacuum energy. [ABSTRACT FROM AUTHOR]

Introduction/purpose: The quantization of the electromagnetic field gives rise to quantum fluctuations which in turn produce a force on macroscopic boundaries. This phenomenon is called the Casimir effect. Method: The second quantization of the electromagnetic field is employed. The Zeta function regularization technique has been applied. Results: Because of the electromagnetic field quantization, a force on macroscopic boundaries is observed. Conclusions: Vacuum fluctuations due to quantum effects give macroscopic results. [ABSTRACT FROM AUTHOR]

A substantial body of phenomenological and theoretical work over the last few years strengthens the possibility that the vacuum energy density (VED) of the universe is dynamical, and in particular that it adopts the 'running vacuum model' (RVM) form, in which the VED evolves mildly as δ ρ vac (H) ∼ ν eff m Pl 2 O H 2 , where H is the Hubble rate and ν eff is a (small) free parameter. This dynamical scenario is grounded on recent studies of quantum field theory (QFT) in curved spacetime and also on string theory. It turns out that what we call the 'cosmological constant', Λ , is no longer a rigid parameter but the nearly sustained value of 8 π G (H) ρ vac (H) around any given epoch H (t) , where G (H) is the gravitational coupling, which can also be very mildly running (logarithmically). Of particular interest is the possibility suggested in past works that such a running may help to cure the cosmological tensions afflicting the Λ CDM. In the current study, we reanalyze the RVM in full and we find it becomes further buttressed. Using modern cosmological data, namely a compilation of the latest SNIa+BAO+ H (z) +LSS+CMB observations, we probe to what extent the RVM provides a quality fit better than the concordance Λ CDM model, with particular emphasis on its impact on the σ 8 and H 0 tensions. We utilize the Einstein–Boltzmann system solver CLASS and the Monte Carlo sampler MontePython for the statistical analysis, as well as the statistical DIC criterion to compare the running vacuum against the rigid vacuum ( ν eff = 0 ). On fundamental grounds, ν eff receives contributions from all the quantized matter fields in FLRW spacetime. We show that with a tiny amount of vacuum dynamics ( ν eff ≪ 1 ) the global fit can improve significantly with respect to the Λ CDM and the mentioned tensions may subside to inconspicuous levels. [ABSTRACT FROM AUTHOR]

I develop a physical picture of dark energy (DE) based on fundamental principles and constants of quantum mechanics (QM) and general relativity (GR) theories. It derives from a conjecture of nonzero masses for nearly standard-model photons or gluons, based on QM localization at a cosmological scale. Dark energy is associated with de Sitter space and that has a fundamentally invariant event horizon, which provides the basis for my DE model. I conceive of DE as a Bose–Einstein condensate (BEC) of cosmologically massive photons, and I estimate fundamentally the binding energy per particle originating from an effectively attractive QM potential in that BEC. Since massive photons may stand at rest in a de Sitter universe with flat spatial geometry, I solve the time-independent Schrödinger equation for a nonrelativistic attractive spherical-well potential self-confining at the de Sitter horizon. The minimal critical potential depth that binds a particle state at the top of that well, combined with the prototypical condition of dark energy-pressure relation in the standard flat Λ -CDM model, provides an estimate of the photon mass, m g . That is supported by an independent calculation of the vacuum energy of the BEC in a de Sitter static metric with coordinate-time slicing. I also consider classical gravitational collapse for a uniform dark energy density, approaching Schwarzschild condition. These QM and GR estimates provide compatible accounts of dark energy condensation, bridging a chasm between nuclear and cosmological scales. I then investigate statistical properties of equilibrium between the g-BEC phase and the ordinary 'vapor' phase of m g photons. Resulting corrections to the Planck spectrum of the CMB are too small to be detectable, at least currently. Most notably, I consider a system of cosmological units, or 'g-units,' that complements the fundamental system of Planck units in various ways. The geometric mean of Planck and g-mass turns out to be remarkably close to current estimates of neutrino masses, suggesting that even masses of the lightest known fermions may be deeply related to both GR and QM fundamental constants Λ , G, c and h. [ABSTRACT FROM AUTHOR]

The fact that quantum gravity does not admit an invariant vacuum state has far-reaching consequences for all physics. It points out that space could not be empty, and we return to the notion of an æther. Such a concept requires a preferred reference frame for describing universe expansion and black holes. Here, we intend to find a reference system or class of metrics that could be attributed to "æther". We discuss a vacuum and quantum gravity from three essential viewpoints: universe expansion, black hole existence, and quantum decoherence. [ABSTRACT FROM AUTHOR]

We suggest that it might be possible to resolve the vacuum energy problem by assuming the reality of a many worlds interpretation of quantum mechanics. The suggested resolution is that the enormous theoretical prediction for the vacuum energy density is actually the value distributed across all the parallel universes in a superposition. It is assumed that branching of all the universes into a larger superposition is a physical process which is extremely rare, but which has occurred sufficiently often since the Big Bang that the discrepancy for the experimentally measured value of the energy density can be explained.

We revisit the calculation of vacuum energy density in compact spacetimes. For the general case of k compact spatial dimensions in p+k dimensional Minkowski spacetime, we calculate the Casimir force on a piston placed in the presence of external electromagnetic fields. We observe that while the presence of a strong external magnetic field reduces the intensity of the Casimir force, the presence of an electric field enhances it instead. We discuss various physical cases and also derive the particle production rate in the presence of such external fields in compact spacetimes. We observe that the pair production rate is enhanced in the presence of a piston.

We heal the cosmological constant problem by means of a cancellation mechanism that adopts a phase transition during which quantum fluctuations are eliminated. To this purpose, we propose that a generalized scalar (dark) matter field with a non-vanishing pressure term can remove the vacuum energy contribution, if its corresponding thermodynamics is written in terms of a quasi-quintessence representation. In such a picture, pressure differs from quintessence as it shows a zero kinetic contribution. Using this field, we investigate a metastable transition phase, in which the Universe naturally passes through an inflationary phase. To reach this target, we single out a double exponential potential, describing the metastable inflationary dynamics by considering suitable boundaries and thermodynamic conditions. We analyze stability investigating saddle, stable and unstable points and we thus predict a chaotic inflation that mimics the Starobinsky exponential potential. Consequently, the role of the proposed dark matter field is investigated throughout the overall Universe evolution. To do so, we provide a physical explanation on unifying the dark sector with inflation by healing the cosmological constant problem. [ABSTRACT FROM AUTHOR]

We considered a vacuum polarization inside a galaxy in the eikonal approximation and found that two possible types of polarization exist. The first type is described by the equation of state p = ρ / 3 , similar to radiation. Using the conformally unimodular metric allows us to construct a non-singular solution for this vacuum "substance" if a compact astrophysical object exists in the galaxy's center. As a result, a "dark" galactical halo appears that increases the rotation velocity of a test particle as a function of the distance from a galactic center. The second type of vacuum polarization has a more complicated equation of state. As a static physical effect, it produces the renormalization of the gravitational constant, thus, causing no static halo. However, a non-stationary polarization of the second type, resulting from an exponential increase (or decrease) of the galactic nuclei mass with time in some hypothetical time-dependent process, produces a gravitational potential, appearing similar to a dark matter halo. [ABSTRACT FROM AUTHOR]

In this discourse, we would like to discuss some issues of concept and principle in the context of the following three aspects. One, how Λ arises as a constant of space–time structure on the same footing as the velocity of light. These are the two constants innate to space–time without reference to any force or dynamics whatsoever, and are interwoven in the geometry of 'free' homogeneous space–time. Two, how does the vacuum energy gravitate? Could its gravitational interaction in principle be included in general relativity or a new theory of quantum space–time/gravity would be required? Finally, we would like to raise the fundamental question: How does the Universe physically expand? Since there does not lie anything outside into which it can expand, instead it has to expand on its own—maybe by creating new space–time out of nothing at each instant and at every location! Thus not only was the Universe created at some instant in the past marking the beginning in the Big Bang, it is in fact being created continuously at each epoch as it expands. We thus need quantum theory of space–time/gravity for fully understanding the working of the Universe. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'. [ABSTRACT FROM AUTHOR]

We would first show that how the two fundamental constants, the velocity of light, c , and the so called, cosmological constant, Λ , arise from geometric characterization of forcefree state of spacetime. They are the two most fundamental constants as they have been synthesized in the structure of spacetime, no other constant can claim this degree of fundamentalness. Next when spacetime turns inhomogeneous, Einstein gravity arises most naturally from the spacetime geometry without any prescription from outside; i.e. the inverse square law is mandated by the geometry, and not a prescription. It would then suggest that dynamics of a fundamental force should not be prescribed but should perhaps be determined by the geometry of appropriate spacetime manifold. [ABSTRACT FROM AUTHOR]

A substantial body of phenomenological and theoretical work over the last few years strengthens the possibility that the vacuum energy density (VED) of the universe is dynamical, and in particular that it adopts the ‘running vacuum model’ (RVM) form, in which the VED evolves mildly as δρvac(H)∼νeffmPl2OH2, where H is the Hubble rate and νeff is a (small) free parameter. This dynamical scenario is grounded on recent studies of quantum field theory (QFT) in curved spacetime and also on string theory. It turns out that what we call the ‘cosmological constant’, Λ, is no longer a rigid parameter but the nearly sustained value of 8πG(H)ρvac(H) around any given epoch H(t), where G(H) is the gravitational coupling, which can also be very mildly running (logarithmically). Of particular interest is the possibility suggested in past works that such a running may help to cure the cosmological tensions afflicting the ΛCDM. In the current study, we reanalyze the RVM in full and we find it becomes further buttressed. Using modern cosmological data, namely a compilation of the latest SNIa+BAO+H(z)+LSS+CMB observations, we probe to what extent the RVM provides a quality fit better than the concordance ΛCDM model, with particular emphasis on its impact on the σ8 and H0 tensions. We utilize the Einstein–Boltzmann system solver CLASS and the Monte Carlo sampler MontePython for the statistical analysis, as well as the statistical DIC criterion to compare the running vacuum against the rigid vacuum (νeff=0). On fundamental grounds, νeff receives contributions from all the quantized matter fields in FLRW spacetime. We show that with a tiny amount of vacuum dynamics (νeff≪1) the global fit can improve significantly with respect to the ΛCDM and the mentioned tensions may subside to inconspicuous levels.

This paper shows the need for the emergence of a universal minimum speed in the space–time by thoroughly investigating Dirac’s large number hypothesis (LNH). We realise that there should be a minimum speed V with the same status of the invariance of the speed of light c. However, V has gravitational origin. Hence, such a minimum speed forms a new kinematic basis in the space–time, leading to a new deformed special relativity (DSR) for the quantum world so-called symmetrical special relativity (SSR). Furthermore, we show that such a new structure of space–time (SSR) reveals a connection between V and a preferred reference frame S V of the background field, leading to the cosmological constant Λ , which can be associated with a cosmological antigravity. We also investigate the effect of the number of baryons N (Eddington number) of the observable Universe on the hydrogen atom. Finally, we show that SSR-metric plays the role of a de-Sitter (dS) metric with a positive cosmological constant, which could assume a tiny value. [ABSTRACT FROM AUTHOR]

The energy of a two-dimensional electron crystal in the low-density limit is studied. The first correction to the electrostatic energy of a crystal is shown to be 1.62733 r s − 3 / 2 Ry. The answer is obtained using the method of numerical integration. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical calculation of the vacuum energy density by summing the contributions of all quantum fields’ vacuum states, which turns out to indicate that there seems to be a missing bosonic contribution in order to match the predictions of the current cosmological models and all observational data to date. The basis for this calculation is a new Zeta function regularization method used to tame the infinities present in the improper integrals of power functions. The paper also presents a few other contributions in the area of vacuum energy.

We present the status of the art of the Archimedes experiment, devoted to measuring the debated interaction of quantum vacuum fluctuations and gravity. The method is essentially the weighing of the transition energy of a layered superconductor where the contribution of vacuum energy to the transition energy is expected to be relevant. The transition is obtained by modulating the temperature of the superconducting sample at a frequency of about 10 mHz and the expected change of weight is measured with a suitably designed high sensitivity cryogenic beam balance. In this paper, we present an overview of the experiment, discussing the expected signal to be measured, and presenting in particular the result of a prototype balance operated in our present laboratory. In the frequency range of the measurement, the sensitivity is affected mainly by seismic, thermal, sensor, and control noise. We discuss these points showing in particular the design of the cryogenic apparatus, the final balance, and the quiet seismic site that will host the final measurement.

The fact that quantum gravity does not admit an invariant vacuum state has far-reaching consequences for all physics. It points out that space could not be empty, and we return to the notion of an æther. Such a concept requires a preferred reference frame for describing universe expansion and black holes. Here, we intend to find a reference system or class of metrics that could be attributed to “æther”. We discuss a vacuum and quantum gravity from three essential viewpoints: universe expansion, black hole existence, and quantum decoherence.

We considered a vacuum polarization inside a galaxy in the eikonal approximation and found that two possible types of polarization exist. The first type is described by the equation of state p=ρ/3, similar to radiation. Using the conformally unimodular metric allows us to construct a non-singular solution for this vacuum “substance” if a compact astrophysical object exists in the galaxy’s center. As a result, a “dark” galactical halo appears that increases the rotation velocity of a test particle as a function of the distance from a galactic center. The second type of vacuum polarization has a more complicated equation of state. As a static physical effect, it produces the renormalization of the gravitational constant, thus, causing no static halo. However, a non-stationary polarization of the second type, resulting from an exponential increase (or decrease) of the galactic nuclei mass with time in some hypothetical time-dependent process, produces a gravitational potential, appearing similar to a dark matter halo.

We propose an inflationary scenario where the inflaton field is non-minimally coupled to spacetime curvature and inflation is driven by a vacuum energy symmetry breaking potential without specifying a priori whether the inflaton field is small or large. As we incorporate vacuum energy into our analysis, we further explore the implications of a non-zero potential offset within inflationary dynamics. We propose that vacuum energy can transform into particles as a result of the transition triggered by spontaneous symmetry breaking. This entails a vacuum energy cancellation that yields an effective cosmological constant during inflation by virtue of a quasi-de Sitter evolution and shows that vacuum energy contribution can manifest as geometric particles produced by inflaton fluctuations, with particular emphasis on super-Hubble modes. We conjecture these particles as quasi-particles arising from interaction between the inflaton and spacetime geometry, enhanced by non-minimal coupling. Specifically, we propose that dark matter arises from a pure geometric quasi-particle contribution, quantifying the corresponding dark matter candidate ranges of mass. In this scenario, we further find that a zero potential offset leads to a bare cosmological constant at the end of inflation, while a negative offset would require an additional kinetic (or potential) contribution in order to be fully-canceled. In this regard, we conclude that the scenario of large-field inflation is preferred since it necessitates a more appropriate selection of the offset. Our conclusion is reinforced as small-field inflation would lead to a significant screening of the Newtonian gravitational constant as inflation ends. [ABSTRACT FROM AUTHOR]

The object of this article is to present the vacuum energy and the dark energy within the framework of the theory of the dynamic medium of reference and to explain the phenomenal difference between the two energies. The dynamic medium is made up of entities (called gravitons) whose vectorial average of speed determines the speed of the flux of the medium at each point in space. It is shown that inside the horizon of black holes (defined by the Schwarzschild radius), the speed of flux is greater than the speed of light, which means that the gravitons themselves have a higher speed to that of light. The quantum entanglement of two photons which propagate in two opposite directions is due to a connection made by gravitons. It is therefore proposed that the gravitons move at the speed VG ≈ Runiverse/tPlanck ≈ 2.4 × 1069 m/s, which makes it possible to guarantee the entanglement of the two photons whatever their position in the Universe and the impossibility to measure the time taken by the influence of a photon to arrive at its twin photon because it is less than the Planck time tPlanck. The expression of the vacuum energy and that of the dark energy within the framework of the theory of the dynamic medium of reference is established. The two expressions Evacuum and Edark and the value of the speed of the most distant galaxies V galaxy make it possible to calculate an approximate value of the speed of the gravitons VG ≈ Vgalaxy...Evacuum Edark ≈ 2.8 × 1069 m/s. This value of the speed of the graviton is very close to that obtained by the quantum entanglement of two photons, which reinforces the existence of nonmaterial entities going at these phenomenal speeds. [ABSTRACT FROM AUTHOR]

In this paper I formulate Minimal Requirements for Candidate Predictions in quantum field theories, inspired by viewing the standard model as an effective field theory. I then survey standard effective field theory regularization procedures, to see if the vacuum expectation value of energy density ( ⟨ ρ ⟩ ) is a quantity that meets these requirements. The verdict is negative, leading to the conclusion that ⟨ ρ ⟩ is not a physically significant quantity in the standard model. Rigorous extensions of flat space quantum field theory eliminate ⟨ ρ ⟩ from their conceptual framework, indicating that it lacks physical significance in the framework of quantum field theory more broadly. This result has consequences for problems in cosmology and quantum gravity, as it suggests that the correct solution to the cosmological constant problem involves a revision of the vacuum concept within quantum field theory. [ABSTRACT FROM AUTHOR]

In this work, we study a spherically symmetric metric in 5D within the framework of Saez-Ballester Theory, where minimal dark energy-matter interaction occurs. We predict that the expanding isotropic universe will be progressively DE dominated. We estimate few values of the deceleration parameter, very close to the recently predicted values. We obtain the value of the DE EoS parameter as ω=−1. Additionally, we measure the value of the overall density parameter as Ω=0.97(≈1), in line with the notion of a close to or nearly (not exactly) flat universe. We predict that the model universe starts with the Big-Bang and ends at the Big Freeze singularity. In general, we cannot find conditions for stabilization of extra dimensions in general relativity, and all dimensions want to be dynamical. Here, we present two possible conditions to solve this stabilization problem in general relativity.

Mereology stands for the philosophical concept of parthood and is based on a sound set of fundamental axioms and relations. One of these axioms relates to the "existence of a universe as a thing having part all other things." The present article formulates this logical expression first as an algebraic inequality and eventually as an algebraic equation reading in words: "The universe equals the sum of all things." "All things" here are quantified by a "number of things." Eventually, this algebraic equation is normalized leading to an expression: "The whole equals the sum of all fractions." This introduces "1" or "100%" as a quantitative--numerical--value describing the "whole." The resulting "basic equation" can then be subjected to a number of algebraic operations. Especially squaring this equation leads to correlation terms between the things implying that the whole is more than just the sum of its parts. Multiplying the basic equation (or its square) by a scalar allows for the comparison to and aligning with physics equations like the entropy equation, the ideal gas equation, an equation for the Lorentz-factor, conservation laws for mass and energy, the energy-mass equivalence, the Boltzmann statistics, and the energy levels in a Hydrogen atom. It further leads to a "contrast equation," which may form the basis for the definition of a length and a time scale. Multiplying the basic equation with vectors, pseudovectors, pseudoscalars, and eventually hypercomplex numbers opens up the realm of possibilities to generate many further equations. [ABSTRACT FROM AUTHOR]

An extended framework of gravity, in which the first Friedmann equation is satisfied up to some constant due to violation of gauge invariance, is tested against astrophysical data: Supernovae Type‐Ia, Cosmic Chronometers, and Gamma‐ray bursts. A generalized expression for the Friedmann equation, including the possible vacuum contributions, is suggested, and two particular cosmological models with two independent parameters are considered within this framework and compared on the basis of the likelihood analysis. One of the models considered includes contribution of the residual vacuum fluctuations to the energy density and places the limit on the UV cutoff scale as kmax=12.43−1.6+0.9[Mp/2+Nsc], where Nsc is the number of minimally coupled scalar fields. Model comparison using the Akaike information criteria and Bayesian evidence shows a preference for the conventional ΛCDM over the extended models. A more general model with three parameters is considered within which an anti‐correlated behavior between the dynamical vacuum fluctuations contribution and a negative cosmological constant was found. The result is an upper limit of ΩΛ≲−0.14 at 95% C.L., which is only mildly disfavored (lnB=−1.8) with respect to ΛCDM. An extended framework of gravity, in which the first Friedmann equation is satisfied up to some constant due to violation of gauge invariance, is tested against astrophysical data: Supernovae Type‐Ia, Cosmic Chronometers, and Gamma‐ray bursts. A generalized expression for the Friedmann equation, including the possible vacuum contributions, is suggested, and two particular cosmological models with two independent parameters are considered within this framework and compared on the basis of the likelihood analysis. Model comparison using the Akaike information criteria and Bayesian evidence shows a preference for the conventional ΛCDM over the extended models. A more general model with three parameters is considered within which an anti‐correlated behavior between the dynamical vacuum fluctuations contribution and a negative cosmological constant was found. [ABSTRACT FROM AUTHOR]

This paper focuses on realistic and timely situations of inflation in connection with the CMB, gravitational and particle physics, adding interdisciplinarity and unification values within a strongly predictive physical approach. The formulation of inflation in the Ginsburg–Landau approach developed by de Vega and Sanchez1 and by Boyanovsky, de Vega, Sanchez and Destri 2 − 7 clarifies and places inflation in the setting of the effective field theories of particle physics. In addition, it sets up a clean way to directly confront the inflationary predictions with the available and forthcoming CMB data and select a definitive model. All CMB + LSS data until now show how powerful is the Ginsburg–Landau effective theory of inflation in predicting observables in agreement with observations, including the inflation energy scale and the inflaton potential, and which has much more to provide in the future. It paves the way to discoveries, new learning and understanding. [ABSTRACT FROM AUTHOR]

We discuss a proposal for a somewhat new formulation of quantum field theory (set in a four-dimensional manifold, the space-time) that includes an analysis of its implications for the evolution of Einstein-Friedmann cosmological models. The proposed theory displays two peculiar features: (i) a local Hilbert-Fock space is associated with each space-time point: we are dealing with a vector bundle whose fibers are Hilbert spaces; the operator-valued sections of the bundle are the quantum fields; (ii) the vacuum energy density is finite, being regularized in a space-time curvature dependent way, independently at each point. In fact everything is finite: self-masses, self-charges, quantum fluctuations: they depend on the space-time curvature and diverge only for a flat metric. In an Einstein-Friedmann model the vacuum (zero-point) energy density is consequently time-dependent and in general not negligible. Then it is shown that, for some choices of the parameters of the theory, the big-bang singularity is resolved and replaced by a bounce driven by the vacuum energy density, which becomes (very) large and negative near the bounce (negative by the contribution of the Fermi fields). But for large times (now, say) the Bose fields' positive vacuum energy eventually overcomes the negative one and we are finally left with the present vacuum energy: positive and reasonably small. [ABSTRACT FROM AUTHOR]

We consider polarizable sheets modeled by a lattice of delta function potentials. The Casimir interaction of two such lattices is calculated at nonzero temperature. The heat kernel expansion for periodic singular background is discussed in relation with the high temperature asymptote of the free energy. [ABSTRACT FROM AUTHOR]

We discuss the Casimir effect in a small cavity, moving in a circular orbit around an Ellis wormhole. We show that the interplay between the spacetime geometry and the cavity orbital motion gives rise to a distortion in the Casimir energy density, causing a reduction of its absolute value. Quite interestingly, such effect can be observed also when the cavity moves on a circular geodesic (albeit unstable) orbit at the wormhole throat, where a comoving observer becomes locally inertial (namely, the observer's reference frame reduces to a geodesic, Fermi-Walker transported one). In that respect, the discussed effect appears as a nonlocal quantum effect by means of which some properties of the underlying spacetime geometry, hidden to local classical measurements, can be captured and unveiled. [ABSTRACT FROM AUTHOR]

It is known that quantum mechanics is one of the most successful theories in physics across the entire history of physics. Nevertheless, many believe that its foundations are still not really understood like: wave-particle duality, interference, entanglement, quantum tunneling, uncertainty principle, wave collapse, vacuum energy, relation between classical mechanics and quantum mechanics, classical limit, quantum chaos, etc., and the continuous failures in the unifying between relativity theory and quantum theory may be an indication about a problem in the foundations. This paper aims at discovering the first small step in the path of solving and understanding these quantum puzzles, in fact, the key to solving quantum puzzles is by understanding the reality of the motion and how it occurs. This paper proposes a model of motion that generalizes the concept of "quantum jump". Actually, we have been able to deduce the principles of quantum mechanics so that the oddity of the quantum puzzles becomes easier to understand and interpret. And as a direct verification of this model of motion this paper deduces the Lamb shift effect without the need of introducing of the concept of vacuum energy fluctuations, and it also discusses that the universal basic law of motion must be broader than both quantum mechanics and classical mechanics. [ABSTRACT FROM AUTHOR]