Vacuum Energy Research Articles

Casimir wormholes in Brans–Dicke theory

In recent years there has been a growing interest in the field of wormhole physics in the presence of Casimir effect. As this effect provides negative energy density, it can be utilized as an ideal candidate for the exotic matter required for creating a traversable wormhole. In the context of modified theories of gravity such as Brans–Dicke (BD) theory (Brans and Dicke 1961 Phys. Rev. 124 925), wormhole geometries have been vastly investigated. However, the scientific literature is silent on the issue of BD wormholes in the presence of Casimir energy. Our aim in the present study is to seek for static spherically symmetric solutions representing wormhole configurations in BD theory with Casimir energy as the supporting matter. The Casimir setup we assume comprises two electrically neutral, infinitely large parallel planes placed in a vacuum. We then consider the Casimir vacuum energy density of a scalar field in such a configuration with Dirichlet and mixed boundary conditions. In the former case the corresponding Casimir force is attractive and in the latter this force is repulsive. We present exact zero tidal force wormhole solutions as well as those with non vanishing redshift function for both types of Casimir energies. The conditions on wormhole solutions along with the weak (WEC) and null (NEC) energy conditions put constraints on the values of BD coupling parameter. These constraints are also subject to the value of BD scalar field at the throat and the throat radius. We therefore find that BD wormholes in the presence of Casimir energy can exist without violating NEC and WEC (for the repulsive Casimir force). Finally, we examine the equilibrium condition for stability of the obtained solutions using Tolman–Oppenheimer–Volkoff equation.

Rindler fluids from gravitational shockwaves

We study a correspondence between gravitational shockwave geometry and its fluid description near a Rindler horizon in Minkowski spacetime. Utilizing the Petrov classification that describes algebraic symmetries for Lorentzian spaces, we establish an explicit mapping between a potential fluid and the shockwave metric perturbation, where the Einstein equation for the shockwave geometry is equivalent to the incompressibility condition of the fluid, augmented by a shockwave source. Then we consider an Ansatz of a stochastic quantum source for the potential fluid, which has the physical interpretation of shockwaves created by vacuum energy fluctuations. Under such circumstance, the Einstein equation, or equivalently, the incompressibility condition for the fluid, becomes a stochastic differential equation. By smearing the quantum source on a stretched horizon in a Lorentz invariant manner with a Planckian width (similarly to the membrane paradigm), we integrate fluctuations near the Rindler horizon to find an accumulated effect of the variance in the round-trip time of a photon traversing the horizon of a causal diamond.

Modified free energy generation using permanent Neodymium Magnet based on Bedini with Maxwell and Lorenz gauge conditions

An efficient, reliable, and real-time electricity generator is proposed by keeping in view the constraints, related to the electricity generation cost, resource reservoirs, greenhouse gas emission, energy storage, and power demand for a pre-defined residential area. Paramount importance is given to the rotor's design; coupled with movable neodymium magnets to increase the harvester's life span and system's net revenue. For the amplification in the stator output, a cost-effective approach is adopted that is based on the parallel winding of the bifilar coil. Furthermore, the coefficient of performance factor for the Bedini's smart school girl circuit based electricity harvester is modified by aiding the concepts of radiant energy incorporated with the electromagnetic phenomenon. Moreover, the mathematical model is formulated by the Maxwell equations using the Lorenz gauge condition to capture free vacuum energy from the environment. For the investigation, analysis, and corroboration of the proposed design, results are reported after performing extensive numerical computations and a comprehensive comparison between the original and modified design is stated in detail.

Gauge invariance, gauge field quantization, and renormalization in autoregularization

Autoregularization, a new divergence-free framework for calculating scattering amplitudes, uses a Lorentz-invariant scale harvested from the kinematics of a scattering process to regularize the amplitude of the process [N. Prabhu, .]. Preliminary validation studies show that autoregularization’s predictions are in good agreement with experimental data—across several scattering processes and a wide range of energy scales. Further, tree-level calculation of the vacuum energy density of the free fields in the Standard Model, using autoregularization, is shown to yield a value that is smaller than the current estimate of the cosmic critical density. In this paper, we prove that the scattering amplitudes in QED, calculated using autoregularization, are gauge invariant. Our proof, which is valid both for autoregularization and current theory, is stronger in that it shows the amplitude of every Feynman diagram is gauge invariant in contrast to previous proofs, which establish gauge invariance only for sum of amplitudes of Feynman diagrams of a process. Next, we show that—unlike in the standard quantization framework, which requires modification of both the quantization framework itself as well as the Lagrangian in order to quantize gauge fields in covariant gauge—in autoregularization the gauge field in QED can be quantized, in covariant gauge, without modifying the standard quantization procedure or the Lagrangian and without introducing the ghost field. Finally, we illustrate renormalization based on autoregularization up to 1-loop in φ4 theory. Since perturbative corrections are finite in autoregularization, the counterterms are not designed to remove divergences but to implement renormalization prescriptions at every order of perturbation. We also derive the renormalization group equation (RGE). Unlike in some regularization schemes (such as dimensional regularization), in which the physical meaning of the fictitious scale introduced by regularization is unclear, in autoregularization the scale in RGE has a transparent physical meaning—it is the Lorentz-invariant kinematic scale of the scattering process of interest. The increasing simplifications resulting within autoregularization and the agreement between its predictions and experimental data, together with the underlying thermodynamic argument, which shows that the framework is essential for a complete description of quantum fields, all converge to suggest that autoregularization provides the proper framework for the description of quantum fields. Published by the American Physical Society 2024

Fractional particle and sigma model

We introduce a classical fractional particle model in ℝn, extending the Newtonian particle concept with the incorporation of the fractional Laplacian. A comprehensive discussion on kinetic properties, including linear momentum and kinetic energy, is provided. We further derive the equations of motion and discuss the symmetries of the system. The Green’s function method is employed to solve the equations of motion in a general case. We illustrate the theory with three important examples: the free fractional particle, the fractional harmonic oscillator, and the charged fractional particle that interacts locally with the electromagnetic field. We use the results of the extension problem by Caffarelli and Silvestre, to construct the associated classical local sigma model for the fractional particle. The sigma model is then quantized using the canonical quantization method, and we compute the vacuum energy at the boundary.

De Sitter-like configurations with asymptotic quintessence environment

We examine a spherically-symmetric class of spacetimes carrying vacuum energy, while considering the influence of an external dark energy environment represented by a non-dynamical quintessence field. Our investigation focuses on a specific set of solutions affected by this field, leading to distinct kinds of spacetime deformations, resulting in regular, singular, and wormhole solutions. We thoroughly discuss the underlying physics associated with each case and demonstrate that more complex deformations are prone to instability. Ultimately, we find that our results lead to an isotropic de Sitter-like solution that behaves as a quintessence fluid. To achieve this, we investigate the nature of the corresponding fluid, showing that it cannot provide the sound speed equal to a constant equation of state parameter near the center. Consequently, we reinterpret the fluid as a slow-roll quintessence by investigating its behavior in asymptotic regimes. Further, we explore the potential implications of violating the isotropy condition on the pressures and we finally compare our findings with the de Sitter and Hayward solutions, highlighting both the advantages and disadvantages of our scenarios.

Anisotropic generalized polytropic spheres: Regular 3D black holes

We model gravitating relativistic 3D spheres composed of an anisotropic fluid in which the radial and transverse components of the pressure correspond to the vacuum energy and a generalized polytropic equation-of-state, respectively. By using the generalized Tolman–Oppenheimer–Volkoff (TOV) equation, and solving the complete system of equations for these anisotropic generalized polytropic spheres, for a given range of model parameters, we find three novel classes of asymptotically AdS black hole solutions with regular core. We show the regularity of the solutions using curvature scalars and the formalism of geodesic completeness. Then, using the eigenvalues of the Riemann curvature tensor, we consider the effects of repulsive gravity in the three static 3D regular black holes, concluding that their regular behavior can be explained as due to the presence of repulsive gravity near the center of the objects. Finally, we study the stability of the regular black holes under the flow of the energy through the Cauchy horizon.

Double-well instantons in finite volume

Assuming a toroidal space with finite volume, we derive analytically the full one-loop vacuum energy for a scalar field tunnelling between two degenerate vacua, taking into account discrete momentum. The Casimir energy is computed for an arbitrary number of dimensions using the Abel-Plana formula, while the one-loop instanton functional determinant is evaluated using the Green’s functions for the fluctuation operators. The resulting energetic properties are non-trivial: both the Casimir effect and tunnelling contribute to the Null Energy Condition violation, arising from a non-extensive true vacuum energy. We discuss the relevance of this mechanism to induce a cosmic bounce, requiring no modified gravity or exotic matter.

Anisotropic Generalization of the ΛCDM Universe Model with Application to the Hubble Tension

Anisotropic Generalization of the ΛCDM Universe Model with Application to the Hubble Tension

ASKING IF VACUUM ENERGY allows COMPUTATIONAL “BITS” PRESENT AT START OF COSMOLOGICAL EVOLUTION, and its possible ties into torsion physics

Based on Torsion as given by de Sabbata and Sirvaram, Erice 1990 . The 1990 article claims that Torsion cancels Cosmological vacuum energy. We consider if relic black holes at the start of inflation may allow for the observed cosmological constant. Using the 1990 text if thermal energy is used at start of inflation creates conceptual issues, whereas an energy term based on Corda’s treatment of black holes may provide a solution. i.e. a left over cosmological constant 10^-121 times vacuum energy . Considerations as to how black hole physics may contribute to torsion and the cosmological constant are considered in several numerical cases Also we present entanglement entropy in the early universe with a shrinking scale factor, due to Muller and Lousto , and show that there are consequences due to initial entanged for a time dependent horizon radius in cosmology, with (flat space conditions) for conformal time . This construction preserves a minimum non zero vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution. The bits are ascribed to initial torsion for reasons which we elaborate on in this manuscript

Constancy of stabilized Randall-Sundrum model with respect to quantum corrections

In the Randall-Sundrum model stabilized with the help of the Goldberger-Wise scalar field, the lowest order vacuum quantum corrections to the energy-momentum tensor of the scalar and tensor fields are calculated. It is shown that the corresponding vacuum energy density of the fields in the bulk leads to the Casimir effect. Using the dimensional regularization method and the Abel-Plana formula, the divergences have been isolated and the vacuum energy density has been renormalized. An analytical expression for the Casimir force is obtained and an estimate of its influence on the model parameters is made. It was found that the quantum corrections lead only to a negligibly small decrease in the distance between the branes, i.e. the model possesses constancy with respect to quantum corrections.

Relativistic generalised uncertainty and the corrected vacuum energy

Abstract In this paper we make use of the recent covariant extension of the generalised uncertainty principle to study the corrections to the vacuum energy of the simplest scalar quantum field theory. We then calculate the modifications to the Casimir effect that such a correction to the vacuum energy would bring about. We emphasise that these corrections are indeed physical.

The dynamics of vacuum, gravity and matter: Implications on the fundamental constants

The possibility that the vacuum energy density (VED) [Formula: see text] 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 [Formula: see text] as a function of the Hubble rate, [Formula: see text], 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.

Non-inertial interpretation of the Dirac oscillator

Non-inertial physics is seldom considered in quantum mechanics and this contrasts with the ubiquity of non-inertial reference frames. Here, we show an application to the Dirac oscillator which provides a fundamental model of relativistic quantum mechanics. The model emerges from a term linearly dependent on spatial coordinates added to the momentum of the free-particle Dirac Hamiltonian. The definition generates peculiar features (mutating vacuum energy, non-Hermitian momentum, accidental degeneracies of the spectrum, etc). We interpret these anomalies in terms of inertial effects. The demonstration is based on the decoupling of the Dirac equation from the stereographic projection that maps the 3D geometry of the dynamical problem to the complex plane. The decoupling shows that the fundamental mechanical model underpinning the Dirac oscillator reduces to the representation of the oscillator in the rotating reference frame attached to the orbital angular momentum. The resulting Coriolis-like contribution to the Hamiltonian accounts for the peculiarities of the model (mutating vacuum energy, form of the non-minimal correction to the momentum, classical intrinsic spin and gain of its quantum value, accidental degeneracies of the energy spectrum, supersymmetric potential). The suggested interpretation has an interdisciplinary character where stereographic geometry, classical physics of the Coriolis effect and quantum physics of Dirac particles contribute to the definition of one of the few exactly soluble models of relativistic quantum mechanics.

Generalized K-essence inflation in Jordan and Einstein frames

We here explore a generalized K-essence model which exhibits characteristics akin to ordinary matter. The inflationary framework proposed aims to unify old with chaotic inflation into a single scheme and it considers minimally and non-minimally coupled scenarios, adopting three classes of potentials, in both Jordan and Einstein frames. We show that, to obtain a suitable amount of particles obtained from vacuum energy conversion during inflation, mitigating the classical cosmological constant problem, large-field inflation and, particularly, the Starobinsky-like class of solutions appears the most suitable one.

Casimir Energy in (2 + 1)-Dimensional Field Theories

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.

The cosmological constant problem and the extra dimensions of [formula omitted]=2 [formula omitted]=5 supergravity

We propose an interpretation for the cosmological constant problem based on modeling the universe as a 3-brane embedded in the bulk of 5-dimensional supergravity with hypermultiplets. When solving the modified Friedmann equations the complex structure moduli of the Calabi-Yau manifold cancel the large value of the vacuum energy density on the brane, wherein this value transfers to an Anti-de Sitter fifth dimensional bulk compactified on a scale (∼10−26m). An effective dark energy density is produced on the brane which equals the observed value responsible for the late-time acceleration of the universe. The bulk undergoes a decelerated contraction while we show that cosmic expansion of the brane-universe consists with the recent observed data of the ΛCDM model. On the other hand, through this model, the hierarchy between the electroweak scale (MEW=100GeV) and the Planck scale (Mpl∼1018GeV) is interpreted by compactifying the 6-extra dimensions of D=5 supergravity on a sub-millimeters scale, where the fundamental scale of gravity within these extra dimensions is MEW.

Is the Euclidean path integral always equal to the thermal partition function?

The Euclidean path integral is compared to the thermal (canonical) partition function in curved static space-times. It is shown that if spatial sections are non-compact and there is no Killing horizon, the logarithms of these two quantities differ only by a term proportional to the inverse temperature, that arises from the vacuum energy. When spatial sections are bordered by Killing horizons the Euclidean path integral is not equal to the thermal partition function. It is shown that the expression for the Euclidean path integral depends on which integral is taken first: over coordinates or over momenta. In the first case the Euclidean path integral depends on the scattering phase shift of the mode and it is UV diverge. In the second case it is the total derivative and diverge on the horizon. Furthermore we demonstrate that there are three different definitions of the energy, and the derivative with respect to the inverse temperature of the Euclidean path integral does not give the value of any of these three types of energy. We also propose the new method of computation of the Euclidean path integral that gives the correct equality between the Euclidean path integral and thermal partition function for non-compact spaces with and without Killing horizon.

Creation of Cosmic Matter Through the Action of the Primordial Cosmic Vacuum Energy

Creation of Cosmic Matter Through the Action of the Primordial Cosmic Vacuum Energy

Motion of test particles in quasi anti-de Sitter regular black holes

In this paper, we explore the characteristics of two novel regular spacetimes that exhibit a nonzero vacuum energy term, under the form of a (quasi) anti-de Sitter phase. Specifically, the first metric is spherical, while the second, derived by applying the generalized Newman–Janis algorithm to the first, is axisymmetric. We show that the equations of state of the effective fluids associated with the two metrics asymptotically tend to negative values, resembling quintessence. In addition, we study test particle motions, illustrating the main discrepancies among our models and more conventional metrics exhibiting non-vanishing anti-de Sitter phase.