Vacuum Energy Research Articles

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

I deduce an exact and analytic Bianchi type I solution of Einstein’s field equations, which generalizes the isotropic ΛCDM universe model to a corresponding model with anisotropic expansion. The main point of the article is to present the anisotropic generalization of the ΛCDM universe model in a way suitable for investigating how anisotropic expansion modifies observable properties of the ΛCDM universe model. Although such generalizations of the isotropic ΛCDM universe model have been considered earlier, they have never been presented in this form before. Several physical properties of the model are pointed out and compared with properties of special cases, such as the isotropic ΛCDM universe model. The solution is then used to investigate the Hubble tension. It has recently been suggested that the cosmic large-scale anisotropy may solve the Hubble tension. I consider those earlier suggestions and find that the formulae of these papers lead to the result that the anisotropy of the cosmic expansion is too small to solve the Hubble tension. Then, I investigate the problem in a new way, using the exact solution of the field equations. This gives the result that the cosmic expansion anisotropy is still too small to solve the Hubble tension in the general Bianchi type I universe with dust and LIVE (Lorentz Invariant Vacuum Energy with a constant energy density, which is represented by the cosmological constant) and anisotropic expansion in all three directions—even if one neglects the constraints coming from the requirement that the anisotropy should be sufficiently small so that it does not have any significant effect upon the results coming from the calculations of the comic nucleosynthesis during the first ten minutes of the universe. If this constraint is taken into account, the cosmic expansion anisotropy is much too small to solve the Hubble tension.

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.

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.

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.

De Sitter-like configurations with asymptotic quintessence environment

Abstract 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 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 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.

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.

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.

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.

Relativistic generalised uncertainty and the corrected vacuum energy

Abstract In this short 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.

Gerstein–Greiner–Zeldovich Effect: Induced Charge Density and Vacuum Energy

Gerstein–Greiner–Zeldovich Effect: Induced Charge Density and Vacuum Energy

Gaussian black holes in brane-world model

We present regular black hole solutions in the framework of Brane-world gravity sourced by a Gaussian matter distribution. The black hole metric shares all the common features of regular black holes in the modified General Relativity (GR) with some exciting features. Considering the energy momentum tensor for an isotropic fluid on the brane, the modified Einstein field equation results with an effective energy momentum tensor that describes an anisotropic fluid determined by brane world parameters. Although the effective radial pressure and energy density satisfy the vacuum energy condition, the effective transverse pressure behaves differently. Gaussian black hole (GBH) solutions are obtained from a Gaussian matter distribution. In the paper, a new class of GBH solutions are obtained in the brane-world gravity with effective normal matter in addition to exotic matter distribution. In the brane world gravity, the mass of a GBH depends on the brane tension. The mass of a GBH formed in the brane world is greater than that at low energy (i.e., GR). We study the trajectories of the massive and the massless particles that can be trapped around a GBH for a set of model parameters. The radii of the photon spheres around the GBH and the condition for the stability of the trajectories of the photon spheres are determined. The properties of the GBHs are studied in detail, including their possible observable features.

Emergent Spacetime and Cosmic Inflation

We present a novel background-independent framework for cosmic inflation, starting with a matrix model. In this framework, inflation is portrayed as a dynamic process responsible for the generation of both space and time. This stands in contrast to conventional inflation, which is characterized as a mere (exponential) expansion of an already existing spacetime, driven by the vacuum energy associated with an inflaton field. We observe that the cosmic inflation is triggered by the condensate of Planck energy into a vacuum and responsible for the dynamical emergence of spacetime. The emergent spacetime picture admits a background-independent formulation so that the inflation is described by a conformal Hamiltonian system which requires neither an inflaton field nor an ad hoc inflation potential. This implies that the emergent spacetime may incapacitate all the rationales to introduce the multiverse hypothesis.

Unraveling Electron Dynamics in p-type Indium Phosphide (100): A Time-Resolved Two-Photon Photoemission Study.

Renewable ("green") hydrogen production through direct photoelectrochemical (PEC) water splitting is a potential key contributor to the sustainable energy mix of the future. We investigate the potential of indium phosphide (InP) as a reference material among III-V semiconductors for PEC and photovoltaic (PV) applications. The p(2 × 2)/c(4 × 2)-reconstructed phosphorus-terminated p-doped InP(100) (P-rich p-InP) surface is the focus of our investigation. We employ time-resolved two-photon photoemission (tr-2PPE) spectroscopy to study electronic states near the band gap with an emphasis on normally unoccupied conduction band states that are inaccessible through conventional single-photon emission methods. The study shows the complexity of the p-InP electronic band structure and reveals the presence of at least nine distinct states between the valence band edge and vacuum energy, including a valence band state, a surface defect state pinning the Fermi level, six unoccupied surface resonances within the conduction band, as well as a cluster of states about 1.6 eV above the CBM, identified as a bulk-to-surface transition. Furthermore, we determined the decay constants of five of the conduction band states, enabling us to track electron relaxation through the bulk and surface conduction bands. This comprehensive understanding of the electron dynamics in p-InP(100) lays the foundation for further exploration and surface engineering to enhance the properties and applications of p-InP-based III-V-compounds for, e.g., efficient and cost-effective PEC hydrogen production and highly efficient PV cells.

Particle production from non-minimal coupling in a symmetry breaking potential transporting vacuum energy

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.

The Vacuum Energy Problem in Quantum Gravity and the Masses of Elementary Particles

The Vacuum Energy Problem in Quantum Gravity and the Masses of Elementary Particles

A thermo-magnetic bag model for the quark-gluon plasma

In this work we study the pressure of the quark-gluon plasma (QGP) in the presence of a weak magnetic field, using a minimally enhanced model of a weakly interacting gas of quasi-particles in a thermal bath. We include the magnetic field effects through the quark mass that has been modified using a recently proposed thermo-magnetic coupling. This thermo-magnetic coupling emerges form the quark-gluon vertex in the HTL approximation [1]. We use Lattice QCD [2] data, to constrain the thermo-magnetic bag function of the quasi-particle model and provide an estimate of the thermo-magnetic vacuum energy density. We then compute the transverse pressure of the system and compare with similar results from the literature. We find that the inverse magnetic catalysis already built within this thermo-magnetic coupling allows a robust description of this Lattice QCD data for the pressure of the QGP in the presence of a weak magnetic field. The extension to the thermal quasi-particle model we have introduced here, makes it easier to pursue further phenomenological studies that require simulations with an EoS that has integrable quasi-particle thermodynamic variables which have the general features of lattice data in the weak magnetic field regime.

Dark energy and matter interacting scenario to relieve H 0 and S 8 tensions* *Supported by the National SKA Program of China (2022SKA0110200, 2022SKA0110203), and the National Natural Science Foundation of China (11975072, 11875102, 11835009)

We consider a new cosmological model (called CDM), in which the vacuum energy interacts with matter and radiation, and test this model using the current cosmological observations. Using the CMB+BAO+SN (CBS) dataset to constrain the model, we find that and tensions are relieved to and , respectively. However, in this case, the CDM model is not favored by the data, compared with ΛCDM. We find that when the and data are added to the data combination, the situation is significantly improved. In the CBS+ case, the model relieves the tension to , and the model is favored over ΛCDM. In the CBS+ + case, we obtain a synthetically best situation, in which the and tensions are relieved to and , respectively. In this case, the model is most favored by the data. Therefore, this cosmological model can greatly relieve the tension and simultaneously effectively alleviate the tension.