Quantum vacuum energy in a closed universe

In preceding papers we have shown that an initial Big-Bang explosion of the universe can not have happened as simply caused by a singularity of extremely hot, highly condensed cosmic matter due to the enhanced centripetal gravity field, enhanced by relativistic cosmic masses [1-3]. Instead, as we argue here, the initial "Bang" must have started from a pressurized cosmic vacuum. We analyse how to adequately describe this cosmic vacuum pressure and how to formulate the initial scale expansion of the universe as a reaction to it. We find that for a needed positive vacuum pressure the thermodynamic polytrope relation between vacuum energy density and vacuum pressure only allows for a range of the vacuum polytrope indices ξ of 3 ˂ ξvac ˂ 5. Furthermore we find that for the preferred value ξvac = 4 one can derive a complete description of the cosmic vacuum energy as function of the cosmic scale and the cosmic time with inclusion of a process of cosmic matter generation by a specific vacuum condensation process producing quantized matter. As result one obtains a matter universe well acquainted to all present day astronomers, however, without the need for an initial, material Big-Bang of a mass singularity. As a surprise, however, the Hubble expansion of the post-recombination universe under the action of cosmic vacuum pressure drives the baryonic distribution function into a more and more non-equilibrium shape with over-Maxwellian-ized populations of the high velocity wings demonstrating surprisingly enough that the cosmic matter temperatures in this expansion phase are in fact increasing, opposite to classical expectations which properly speaking would clearly predict adiabatic temperature decreases.

In preceding papers we have shown that an initial Big-Bang explosion of the universe can not have happened as caused by a singularity of extremely hot cosmic matter due to the centripetal gravity field enhanced by relativistic mass [1,2]. Instead it must have started from a pressurized cosmic vacuum. In this article here we shall analyse how to adequately describe this cosmic vacuum pressure and how to formulate the initial scale expansion of the universe as reaction to its action. We find that for a needed positive vacuum pressure the thermodynamic polytrope relation between vacuum energy density and vacuum pressure only allows for a range of the vacuum polytrope indices ξ of 3 ˂ ξvac ˂ 5. Furthermore we find that for the preferred value ξvac = 4 one can derive a complete description of the cosmic vacuum energy as function of the cosmic scale and the cosmic time with inclusion of a process of cosmic matter generation by a specific vacuum condensation process producing quantized matter. As result one obtains a matter universe well aquainted to all present day astronomers, however, without the need for an initial, material Big-Bang

The accelerating expansion of the Universe points to a small positive vacuum energy density and negative vacuum pressure. A strong candidate is the cosmological constant in Einstein's equations of general relativity. Possible contributions are zero-point energies and the condensates associated with spontaneous symmetry breaking. The vacuum energy density extracted from astrophysics is 1056 times smaller than the value expected from quantum fields and standard model particle physics. Is the vacuum energy density time dependent? We give an introduction to the cosmological constant puzzle and ideas how to solve it.

We consider a nonsingular origin for the universe starting from an Einstein static universe, the so-called "emergent universe" scenario, in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field ϕ are considered in the action. The first-order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (SSB) of scale invariance (SI). After SSB of SI, it is found that a nontrivial potential for the dilaton is generated. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe, followed by an inflationary phase and ϕ → -∞, describing our present universe. The dynamics of the scalar field becomes nonlinear and these nonlinearities produce a nontrivial vacuum structure for the theory and are responsible for the stability of some of the emergent universe solutions, which exists for a parameter range of values of the vacuum energy in ϕ → -∞, which must be positive but not very big, avoiding the extreme fine tuning required to keep the vacuum energy density of the present universe small. The nontrivial vacuum structure is crucial to ensure the smooth transition from the emerging phase, to an inflationary phase and finally to the slowly accelerated universe now. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.

In this work we investigate if the interaction of the Kerr–Taub–NUT spacetime with test scalar and neutrino fields can lead to the destruction of the event horizon. It turns out that both extremal and nearly extremal black holes can be destroyed by scalar and neutrino fields if the initial angular momentum of the spacetime is sufficiently large relative to its mass and NUT charge. This is the first example in which a classical field satisfying the null energy condition can actually destroy an extremal black hole. For scalar fields, the modes that can lead to the destruction of the horizon are restricted to a narrow range due to superradiance. Since superradiance does not occur for neutrino fields, the destruction of the horizon by neutrino fields is generic, and it cannot be fixed by backreaction effects. We also show that the extremal black holes that can be destroyed by scalar fields correspond to naked singularities in the Kerr limit, in accord with the previous results which imply that extremal Kerr black holes cannot be destroyed by scalar test fields.

Perfectly conducting boundaries, and their Dirichlet counterparts for quantum scalar fields, predict nonintegrable energy densities. A more realistic model with a finite ultraviolet cutoff yields two inconsistent values for the force on a curved or edged boundary (the ``pressure anomaly''). A still more realistic, but still easily calculable, model replaces the hard wall by a power-law potential; because it involves no a posteriori modification of the formulas calculated from the theory, this model should be anomaly free. Here we first set up the formalism and notation for the quantization of a scalar field in the background of a planar soft wall, and we approximate the reduced Green function in perturbative and WKB limits (the latter being appropriate when either the mode frequency or the depth into the wall is sufficiently large). Then we display numerical calculations of the energy density and pressure for the region outside the wall, which show that the pressure anomaly does not occur there. Calculations inside the wall are postponed to later papers, which must tackle the regularization and renormalization of divergences induced by the potential in the bulk region.

Inflation has presented solutions for a number of important cosmological problems while leaving some unanswered. In this paper, we present a new cosmological model based on the quantization of the zero-point field, which is consistent with empirical data, requires fewer assumptions, and presents answers to some of those unanswered questions. A comparison between standard cosmology and the theory presented in this paper is given herein. Vacuum energy density: The standard inflationary model needs both Hubble’s constant and matter density to estimate the vacuum energy density, but new cosmological model needs only Hubble’s constant. Non-vacuum energy density: The standard model cannot predict the non-vacuum energy density, but the new model can predict it using only Hubble’s constant. Ratio of vacuum energy to total energy: The standard model cannot predict the ratio of vacuum energy to total energy, but the new model can predict it, without using Hubble’s constant. Energy conservation: In the standard model, total energy is not conserved before inflation and at the time of the creation of the universe, but in the new model total energy is mathematically proved to be conserved from the beginning of the universe as net energy (including gravitational potential energy) is always zero. Flatness and homogeneity: The standard model requires an inflaton field with a specific potential energy distribution to explain it, but the new model does not need any such hypothetical field; the zero-point field is sufficient.

We consider the vacuum energy of massive quantum fields in an expanding universe. We define a conserved renormalized energy-momentum tensor by means of a comoving cutoff regularization. Using exact solutions for de Sitter space-time, we show that in a certain range of mass and renormalization scales there is a contribution to the vacuum energy density that scales as nonrelativistic matter and that such a contribution becomes dominant at late times. By means of the WKB approximation, we find that these results can be extended to arbitrary Robertson-Walker geometries. We study the range of parameters in which the vacuum energy density would be compatible with current limits on dark matter abundance. Finally, by calculating the vacuum energy in a perturbed Robertson-Walker background, we obtain the speed of sound of density perturbations and show that the vacuum energy density contrast can grow on sub-Hubble scales as in standard cold dark matter scenarios.

In this paper we discuss the solutions of the c-number quantum-mechanical equations of neutrino, Maxwell, and scalar fields in the background metric of a static, cylindrically symmetric magnetic or plasm universe. The magnetic universe consists of a parallel magnetic field distribution held together by the gravitational field of its own energy and stress. It is an exact solution of the Einstein–Maxwell equations for the gravitational field associated with a stationary source-free cylindrically symmetric magnetic field. The solution does not depend specifically upon the assumption that the seat of the energy-stress distribution is an electromagnetic field. A ’’plasm of index 2’’ would have the same metric. The main instrument of the present perturbation theory, valid in all algebraically special spacetimes, is the Cohen–Kegeles (CK) scalar wave equation for test fields of helicity h (or s). This equation, written in the updated Geroch–Held–Penrose (GHP) formalism, is made explicit for the chosen null tetrad by determining the spin coefficients and the operators of that formalism. Exact solutions of the CK wave equation are obtained for the case of zero orbital angular momentum. For the case of nonzero orbital angular momentum the JWKB approximation is used to obtain the quadratures for the orbits in the magnetic universe. It is shown that the neutrino orbits precess about the magnetic (or plasm) universe axis in a manner different from orbits of particles with helicity zero and helicity one. The expression for the neutrino precessional frequency (due to nonvanishing helicity) is given explicitly. The photon precessional frequency is twice that for neutrinos. Finally, the CK procedure is compared with that of Teukolsky for finding the neutrino and Maxwell fields in type D spacetimes.

We propose a unified framework for dark matter and dark energy based on the thermodynamic properties of a degenerate, relativistic Fermi gas in a higher-dimensional space-time. Extending the standard equation of state to D -dimensional space-time, we derive analytical expressions for the energy density, pressure, number density, sound velocity, and polytropic indices of a zero-temperature Fermi gas. Remarkably, we show that in the limit of vanishing Fermi momentum, the system exhibits a negative vacuum pressure and positive energy density when $$D=(5+4n)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mo>(</mml:mo> <mml:mn>5</mml:mn> <mml:mo>+</mml:mo> <mml:mn>4</mml:mn> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , with $$n\in \mathbb {N}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> . This feature provides a natural mechanism for the emergence of a cosmological constant-like component from fermionic matter in extra dimensions. In this context, dark matter arises from the bulk fermions’ rest mass energy, while dark energy emerges from their vacuum contributions. The observed cosmological vacuum energy density can be matched by fixing the compactification length scale, leading to constraints that depend on the fermion mass and the number of extra dimensions. Our results suggest that the dark sector may originate from a common fermionic source embedded in a higher-dimensional space-time, offering a novel pathway toward the unification of dark matter and dark energy.

An Eötvös experiment to test the weak equivalenceprinciple (WEP) for zero-point vacuum energy is proposed using asatellite. Following the suggestion of Ross for a terrestrialexperiment of this type, the acceleration of a spherical testmass of aluminium would be compared with that of a similar testmass made from another material. The estimated ratio of thezero-point vacuum energy density inside the aluminium sphere tothe rest mass energy density is ~1.6×10-14,which would allow a 1% resolution of a potential WEP violationobserved in a satellite mission test that had a baselinesensitivity to WEP violations of ~10-16. An observedviolation of the WEP for vacuum energy density would constitutea significant clue as to the origin of the cosmological constantand the source of dark energy, and test a recently proposedresolution of the cosmological constant problem, based on amodel of nonlocal quantum gravity and quantum field theory.

The physical understanding of the real mechanism of gravity is one of the most important questions in Physics. As we have already shown in a previous paper, the rest and relativistic mass of an elementary particle or body can be considered as having their origin in the diminished energy density of a Quantum Vacuum, characterized by a granular structure quantized through a Planck metric. The presence of massive bodies, from the scale of elementary particles to that of stellar objects and black holes, then determines Quantum Vacuum energy density gradients. In this paper we have proposed a novel physical model in which gravity is generated by the pressure of Quantum Vacuum in the direction of its own higher to lower density due to the presence of material objects or particles. In this picture gravity is an immediate and not – propagating action – at – a – distance interaction, resulting from the Quantum Vacuum dynamics, in turn related to fundamental properties of space itself only, not requiring the existence of the hypothetical graviton. Furthermore, the possibility to consider this Quantum Vacuum as a Bose – Einstein like condensate allows us to recover the large – scale description of the Universe consistent with General Relativity, viewed as the long – wavelength geometro – hydrodynamic limit of the Quantum Vacuum dynamics. The proposed model is also able to give a very simple explanation of: the equivalence between inertial and gravitational mass, the origin and dynamical behavior of dark matter and dark energy, the physical meaning of singularity in black hole, as well as to overcome some of the main difficulties of the Higgs model. Finally this model of gravity can be used as a starting point for a novel interpretation of the recently published data of BICEP2 radio telescope about the presumed indirect observation of gravitational wave

In the Hamiltonian formulation of General Relativity the energy associated to an asymptotically flat space-time with metric $g_{\mu\nu}$ is related to the Hamiltonian $H_{GR}$ by $E=H_{GR}[g_{\mu\nu}]-H_{\rm GR}[\eta_{\mu\nu}]$, where the subtraction of the flat-space contribution is necessary to get rid of an otherwise divergent boundary term. This classic result indicates that the energy associated to flat space does not gravitate. We apply the same principle to study the effect of zero-point fluctuations of quantum fields in cosmology, proposing that their contribution to the cosmic expansion is obtained computing the vacuum energy of quantum fields in a FRW space-time with Hubble parameter $H(t)$ and subtracting from it the flat-space contribution. [...] After renormalization, this produces a renormalized vacuum energy density $\sim M^2H^2(t)$, where $M$ is the scale where quantum gravity sets is, so for $M$ of order of the Planck mass a vacuum energy density of the order of the critical density can be obtained without any fine tuning. The counterterms can be chosen so that the renormalized energy density and pressure satisfy $p=w\rho$, with $w$ a parameter that can be fixed by comparison to the observed value, so in particular one can chose $w=-1$. An energy density evolving in time as $H^2(t)$ is however observationally excluded as an explanation for the dominant dark energy component which is responsible for the observed acceleration of the universe. We rather propose that zero-point vacuum fluctuations provide a new subdominant "dark" contribution to the cosmic expansion that, for a UV scale $M$ slightly smaller than the Planck mass, is consistent with existing limits and potentially detectable.

We have shown in recent papers (see Fahr, 2023, Fahr and Heyl, 2023) that the original explosion of the universe cannot have had its origin in a mass singularity of relativistically superhot cosmic matter, since the associated extremely strong centripetal gravitational field would clearly have impeded the Big-Bang to happen. As we suggest instead, the so called paradigmatic "Big-Bang", if it at all ever happened, must rather be caused by something like a positively pressurized primordial cosmic vacuum, but not by a singularity-condensed cosmic matter. The question, however, then is, how a cosmic vacuum in physical terms has to be constituted that drives the initial explosion of the universe as expected into a Hubble – expansion, and, while doing so, in addition generates that amount of cosmic matter which in the present days of our universe evidently is all around us and thus needs to have its non-singular origin later in the evolution of the universe? As we do show here in this article, this requires a positively pressurized vacuum with pvac = pvac (εvac) ≥ 0 and a vacuum energy density εvac that, while performing thermodynamic work at the expansion of the universe, decreases with the increase of the scale R of the universe. This, however, is different to the well known ΛCDM -model with a constant vacuum energy density which is presently in favour. On the basis of the general energy conservation law we do formulate a relation here, that describes the condensation of quantized energy structures in form of elementary masses out of the energized vacuum. While the relative energy density of vacuum-condensed masses ρm/ρvac is permanently increasing with world time t, the energy density of the vacuum itself permanently decreases. In this paper we look for solutions which on the basis of these procedures just lead to the structures which evidently appear in our present-day universe. Not yet solved, though touched by us in this paper here, is the question whether or not the elementary abundances of the condensed cosmic matter under these conditions also would match the astrophysical observations

In recent papers by Fahr (2023) and Fahr and Heyl (2024) we had shown that an instantaneous, initial Big-Bang explosion of a purely material universe can not have happened [1,2]. At least not by itself, as is most often envisioned, any way not solely caused by the enormous pressure of the matter in the singularity of the initially extremely hot, highly condensed cosmic matter. This is due to the strongly enhanced centripetal gravity field, increased by the gravitating mass of the relativistic, kinetic cosmic masses. where by the anticipated explosive action of the material pressure is nullified. Instead, as was argued by us, the initial "Bang" rather must have started from a pressurized cosmic vacuum with its explosive pressure, otherwise a "Bang" never could have happened. In the above mentioned papers we thus analysed how to adequately describe this cosmic vacuum pressure and how to formulate the initial scale expansion of the universe, occuring solely on the basis of that newly considered, cosmic ingredient. Thereby it became evident that for a needed positive vacuum pressure the thermodynamic polytrope relation between vacuum energy density ρvac and vacuum pressure pvac for the purpose of a cosmic scale expansion Ṙ &gt; 0 only allows for a very limited range of vacuum polytrope indices ξ of 3 &lt; ξvac &lt; 5. For the prefered value ξvac = 4, one can derive a complete description of the cosmic vacuum energy as function of the cosmic scale R and the cosmic time t with inclusion of a process of cosmic matter generation in the course of the cosmic expansion by a specific vacuum condensation process producing a material universe for the later expansion phases. As result one so far obtains a matter universe well familiar to all present day astronomers, however, without the need for an initial, purely material Big-Bang of a mass singularity. The aspect which was not carefully taken into account so far is the cosmologic importance of the initially relativistically hot cosmic matter and its genuine thermodynamics. This shall become the new subject here. As a surprise, however, in any case the Hubble expansion of the post-recombination universe under the action of cosmic vacuum pressure drives the baryonic distribution function into a more and more non-equilibrium shape with over-Maxwellian populations of the high velocity wings demonstrating surprisingly enough that the cosmic matter temperatures in this expansion phase are in fact increasing with scale R, opposite to classical expectations which, strictly speaking, would predict adiabatic temperature decreases. We determine the distribution function of cosmic gases in this expansion phase and find that structure formation must have run different from what is presently thought