Vacuum Energy Research Articles

On the cosmological constant in the deformed Einstein–Cartan gauge gravity in De Donder–Weyl Hamiltonian formulation

AbstractA modification of the Einstein–Hilbert theory, the Covariant Canonical Gauge Gravity (CCGG), leads to a cosmological constant that represents the energy of the space–time continuum when deformed from its (A)dS ground state to a flat geometry. CCGG is based on the canonical transformation theory in the De Donder–Weyl (DW) Hamiltonian formulation. That framework modifies the Einstein–Hilbert Lagrangian of the free gravitational field by a quadratic Riemann–Cartan concomitant. The theory predicts a total energy‐momentum of the system of space–time and matter to vanish, in line with the conjecture of a “Zero‐Energy‐Universe” going back to Lorentz (1916) and Levi‐Civita (1917). Consequently, a flat geometry can only exist in presence of matter where the bulk vacuum energy of matter, regardless of its value, is eliminated by the vacuum energy of space–time. The observed cosmological constant Λobs is found to be merely a small correction attributable to deviations from a flat geometry and effects of complex dynamical geometry of space–time, namely torsion and possibly also vacuum fluctuations. That quadratic extension of General Relativity, anticipated already in 1918 by Einstein, thus provides a significant and natural contribution to resolving the “cosmological constant problem”.

The potential of direct air capture using adsorbents in cold climates.

Global warming threatens the entire planet, and solutions such as direct air capture (DAC) can be used to meet net-zero goals and go beyond. This study investigates using DAC in a 5-step temperature vacuum swing adsorption (TVSA) cycle with adsorbents' Li-X and Na-X, readily available industrial zeolites, to capture and concentrate CO2 from air in cold climates. From this study, we report that Na-X in cold conditions has the highest known CO2 adsorption capacity in air of 2.54mmol/g. This combined with Na-X's low CO2 heat of adsorption, and fast uptake-rate in comparison to other benchmark materials, allowed for Na-X operating in cold conditions to have the lowest reported DAC operating energy of 1.1 MWh/tonCO2. These findings from this study show the promise of this process in cold climates of Canada, Alaska, Greenland, and Antarctica to be part of the solution to global warming.

Flat JT gravity and the BMS-Schwarzian

We consider Minkowskian Jackiw-Teitelboim (JT) gravity in Bondi gauge at finite temperature, with non-zero vacuum energy. Its asymptotic symmetries span an extension of the warped Virasoro group, dubbed ‘BMS2’, which we investigate in detail. In particular, we show that this extension has a single coadjoint orbit when central charges are real and non-zero. The ensuing BMS-Schwarzian action has no saddle points, and only coincides with the boundary action functional of flat JT gravity up to a crucial dilatonic zero-mode that ensures the existence of a well-defined bulk variational principle. We evaluate the corresponding gravitational partition function, which turns out to be one-loop exact precisely thanks to the presence of such a zero-mode.

Multiple Transitions in Vacuum Dark Energy and H 0 Tension

We study the effects of multiple transitions in the vacuum dark energy density on the H 0 tension problem. We consider a phenomenological model in which the vacuum energy density undergoes multiple transitions in the early as well as the late universe and compare the model’s predictions using the three sets of data from the cosmic microwave background, baryonic acoustic oscillations, and supernovae. The transient dark energy can be either positive (dS-like) or negative (AdS-like). We conclude that a transient late-time AdS-type vacuum energy typically yields the higher value of H 0, which can alleviate the H 0 tension. In addition, to obtain a value of H 0 comparable to the value obtained from the local cosmological measurements the spectral index n s moves toward its Harrison–Zel’dovich scale-invariant value.

Varying-G gravity: physical properties, asymptotic regimes, and Green’s functions, an event horizon, the vacuum energy density, and the external pressure that modifies Jeans stability

ABSTRACT We study varying-G gravity and we add the necessary proofs (general force law, asymptotic forms, and Green’s functions, vacuum and external pressures, linearization of perturbations leading to a new Jeans stability criterion, and a physical origin) to elevate this novel idea to the status of a classical theory. The theory we lay out is not merely a correction to Newtonian gravity, it is a brand-new theory of gravity that encompasses the Newtonian framework and weak-field Weyl gravity in the limit of high accelerations, as well as Modified Newtonian Dynamics (MOND) in the opposite limit. In varying-G gravity, the source of the potential of a spherical mass distribution M(x) is σ(dG/dx) + (G/x2)(dM/dx), where x is the dimensionless radial coordinate and σ(x) = M(x)/x2 is the surface density away from the center x = 0. We calculate the potential $\Phi (x)=\int {G(x)\, \sigma (x)\, dx}$ from Poisson’s equation and the radial acceleration $a(x) = G(x)\, \sigma (x)$. Furthermore, a non-linear scaling transformation of the radial coordinate $x\in (0, \infty)\longmapsto \xi \in (0, 1)$ with scale factor ξ/x ∝ 1/G produces a finite space, in which the spherical surface ξ = 1 is an event horizon. In this classical context, it is the coupling of σ(x) to the gradient dG/dx in the above source that modifies the dynamics at all astrophysical scales, including empty space (where dG/dx ≠ 0). In vacuum, the source σ(dG/dx) supports an energy density distribution that supplies a repelling pressure gradient outside of discrete isolated massive systems. Surprisingly, the same source becomes attractive in linearized perturbations, and its linear pressure gradient opposes the kinetic terms in the Jeans stability criterion.

Early and late time cosmology: the f(R) gravity perspective

Discrepancies between observations at early and late cosmic epochs, and the vacuum energy problem associated with the interpretation of cosmological constant, are questioning the $\Lambda$CDM model. Motivated by these conceptual and observational facts, extensions of Einstein's gravity are recently intensively considered in view of curing unsolved issues suffered by General Relativity at ultraviolet and infrared scales. Here, we provide a short overview of some aspects of $f(R)$ gravity, focusing, in particular, on cosmological applications. Specifically, Noether symmetries are adopted as a criterion to select viable models and investigate the corresponding dynamics. We thus find solutions to the cosmological field equations, analyzing the behaviour of selected models from the matter-dominated to the present epoch. Moreover, constraints coming from energy conditions and the so-called swampland criteria are also considered. In particular, we qualitatively discuss the possibility of $f(R)$ gravity to account for fixing cosmic tensions.

Thermal Casimir Effect in the Einstein Universe with a Spherical Boundary

In the present paper, we investigate thermal fluctuation corrections to the vacuum energy at zero temperature of a conformally coupled massless scalar field, whose modes propagate in the Einstein universe with a spherical boundary, characterized by both Dirichlet and Neumann boundary conditions. Thus, we generalize the results found in the literature in this scenario, which has considered only the vacuum energy at zero temperature. To do this, we use the generalized zeta function method plus Abel-Plana formula and calculate the renormalized Casimir free energy as well as other thermodynamics quantities, namely, internal energy and entropy. For each one of them, we also investigate the limits of high and low temperatures. At high temperatures, we found that the renormalized Casimir free energy presents classical contributions, along with a logarithmic term. Also in this limit, the internal energy presents a classical contribution and the entropy a logarithmic term, in addition to a classical contribution as well. Conversely, at low temperatures, it is demonstrated that both the renormalized Casimir free energy and internal energy are dominated by the vacuum energy at zero temperature. It is also demonstrated that the entropy obeys the third law of thermodynamics.

Toolkit for scalar fields in universes with finite-dimensional Hilbert space

The holographic principle suggests that the Hilbert space of quantum gravity is locally finite-dimensional. Motivated by this point-of-view, and its application to the observable Universe, we introduce a set of numerical and conceptual tools to describe scalar fields with finite-dimensional Hilbert spaces, and to study their behaviour in expanding cosmological backgrounds. These tools include accurate approximations to compute the vacuum energy of a field mode k as a function of the dimension d k of the mode Hilbert space, as well as a parametric model for how that dimension varies with |k|. We show that the maximum entropy of our construction momentarily scales like the boundary area of the observable Universe for some values of the parameters of that model. And we find that the maximum entropy generally follows a sub-volume scaling as long as d k decreases with |k|. We also demonstrate that the vacuum energy density of the finite-dimensional field is dynamical, and decays between two constant epochs in our fiducial construction. These results rely on a number of non-trivial modelling choices, but our general framework may serve as a starting point for future investigations of the impact of finite-dimensionality of Hilbert space on cosmological physics.

The effective theory of gravity and dynamical vacuum energy

Gravity and general relativity are considered as an Effective Field Theory (EFT) at low energies and macroscopic distances. The effective action of the conformal anomaly of light or massless quantum fields has significant effects on macroscopic scales, due to associated light cone singularities that are not captured by an expansion in local curvature invariants. A compact local form for the Wess-Zumino effective action of the conformal anomaly and stress tensor is given, requiring the introduction of a new light scalar field, which it is argued should be included in the low energy effective action for gravity. This scalar conformalon couples to the conformal part of the spacetime metric and allows the effective value of the vacuum energy, described as a condensate of an exact 4-form abelian gauge field strength F = dA, to change in space and time. This is achieved by the identification of the torsion dependent part of the Chern-Simons 3-form of the Euler class with the gauge potential A, which enters the effective action of the conformal anomaly as a J · A interaction analogous to electromagnetism. The conserved 3-current J describes the worldtube of 2-surfaces that separate regions of differing vacuum energy. The resulting EFT thus replaces the fixed constant Λ of classical gravity, and its apparently unnaturally large sensitivity to UV physics, with a dynamical condensate whose ground state value in empty flat space is Λeff = 0 identically. By allowing Λeff to vary rapidly near the 2-surface of a black hole horizon, the proposed EFT of dynamical vacuum energy provides an effective Lagrangian framework for gravitational condensate stars, as the final state of complete gravitational collapse consistent with quantum theory. The possible consequences of dynamical vacuum dark energy for cosmology, the cosmic coincidence problem, and the role of conformal invariance for other fine tuning issues in the Standard Model are discussed.

Reheating after relaxation of large cosmological constant

We present a cosmological model of an early-time scenario that incorporates a relaxation process of the would-be large vacuum energy, followed by a reheating era connecting to the standard hot big bang universe. Avoiding fine-tuning the cosmological constant is achieved by the dynamics of a scalar field whose kinetic term is modulated by an inverse power of spacetime curvature [1,2]. While it is at work against radiative corrections to the dark energy, this mechanism alone would wipe out not only the vacuum energy but also all other matter contents. Our present work aims to complete the scenario by exploiting a null-energy-condition violating sector whose energy is eventually transferred to a reheating sector. We provide an explicit example of this process and thus a concrete scenario of the cosmic onset that realizes the thermal history of the Universe with a negligible cosmological constant.

A Possible Solution of the Cosmological Constant Problem Based on GW170817 and Planck Observations with Minimal Length Uncertainty

We propose generalized uncertainty principle (GUP) with an additional term of quadratic momentum motivated by string theory and black hole physics and providing a quantum mechanical framework for the minimal length uncertainty, at the Planck scale. We demonstrate that the GUP parameter, β 0 , could be best constrained by the gravitational wave observations, GW170817 event. To determine the difference between the group velocity of graviton and that of the light, we suggest another proposal based on the modified dispersion relations (MDRs). We conclude that the upper bound of β 0 reads ≃1060. Utilizing features of the UV/IR correspondence and the apparent similarities between GUP (including nongravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant Λ (obviously manifesting gravitational influences on the vacuum energy density), known as catastrophe of nongravitating vacuum, we suggest a possible solution for this long-standing physical problem, Λ ≃ 1 0 − 47 GeV4/ℏ3c3.

Revisiting vacuum energy in compact spacetimes

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.

Dynamical systems of cosmological models for different possibilities of G and rho _{Lambda }

The present paper deals with the dynamics of spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model with a time varying cosmological constant Lambda where Lambda evolves with the cosmic time t through the Hubble parameter H, that is, Lambda (H). We use the expression of Lambda (H) in the form of Taylor series with respect to H keeping only the even powers of H because of the general covariance of the effective action of quantum field theory in a curved background. Dynamical systems for three different cases based on the possibilities of gravitational constant G and the vacuum energy density rho _{Lambda } have been analysed. In Case I, both G and rho _{Lambda } are taken to be constant. We analyse stability of the system by using the notion of spectral radius, behavior of perturbation along each of the axes with respect to cosmic time and Poincaré sphere. In Case II, we have dynamical system analysis for G=hbox {constant} and rho _{Lambda } ne constant where we study stability by using the concept of spectral radius and perturbation function. In Case III, we take G ne constant and rho _{Lambda } ne constant where we introduce a new set of variables to set up the corresponding dynamical system. We find out the fixed points of the system and analyse the stability from different directions: by analysing behaviour of the perturbation along each of the axes, Center Manifold Theory and stability at infinity using Poincaré sphere respectively. Phase plots and perturbation plots have been presented. We deeply study the cosmological scenario with respect to the fixed points obtained and analyse the late time behavior of the Universe. The effective equation of state parameter omega _{eff}, total energy density Omega _{tt} are also evaluated at the fixed points for each of the three cases and these values are in agreement with the observational values in Aghanim et al. (Astron Astrophys 641(A6): 2020, 2018). We have also presented the EoS parameter for dark energy sector omega _{de}(z_{r}), the Hubble parameter H(z_{r}) and the deceleration parameter q(z_{r}) as functions of redshift z_{r} for all the three cases and their plots over redshift are also provided. We analyse the quintessence-like, phantom-like or the purely cosmological-constant type dark energy, etc behavior when the EoS approaches the fixed point value near -1. The present values of omega _{de}(z_{r}), H(z_{r}), q(z_{r}) and z_{rt} have been tabulated in Table 4 and they fall within the range of cosmological observations. The transition redshift value (z_{rt}) for each of the three cases have also been evaluated. In each of the cases the developed model agrees with the fact that the Universe is in the epoch of accelerated expansion for suitable values of free parameters chosen. The developed cosmological models associated with each of the three cases have a deep connection with the accelerated expansion phenomena of the evolving Universe.

A minimal self-tuning model to solve the cosmological constant problem

The expansion of the Universe is observed to be accelerating, with the simplest solution being a classical cosmological constant. However, this receives contributions from the quantum vacuum, which are predicted to be many orders of magnitude larger than observations, and suffers from radiative instabilities requiring repeated fine-tuning. In this paper we present a minimal, self-tuning scalar field model that can dynamically cancel a large quantum vacuum energy, avoiding Weinberg's No-Go Theorem, and produce accelerated de Sitter expansion at a lower energy scale as a solution to the problem. Our minimal model, which contains a non-canonical kinetic energy and a linear potential, belongs to the Kinetic Gravity Braiding sub-class of Horndeski theory which is not observationally excluded, and lies outside of the known Fab-Four or Well-Tempered models. We find analytic solutions in the limits of slow-roll and fast-roll, and numerically solve the equations of motion to illustrate our model. We show that the model allows for a matter dominated era, and that the attractor solution is stable under a phase transition in the vacuum energy density. We also consider the energy-scales required to match observations. Our model shows the existence of a wider class of successful self-tuning models than previously assumed.

Self-tuning of the cosmological constant in brane-worlds with P(X,ϕ)

We revisit the idea of self-tuning the observed cosmological constant to a vanishing value and promote it to a selection criterion of brane-world models, in which our Universe is described by a 3-brane embedded in a 5d bulk. As a concrete setup, we consider a bulk scalar field ϕ described by a general Lagrangian P(X,ϕ) with X = -(∂ϕ)2/2. By requiring that the model enforces the 4d curvature of the maximally symmetric 3-brane world-volume to vanish independently of the 4d effective vacuum energy, only two possibilities remain: one with a canonical bulk kinetic term and the other with an unconventional bulk kinetic term similar to a Cuscuton field. Further demanding the absence of bulk singularity, the latter is selected as a unique possibility within the class of models. At the background level, the solution can accommodate any warp factor profile free from bulk singularity and with a finite effective 4d Planck mass. In a cosmological context, our solution would describe our (almost) flat Universe at late times, with a bulk warp factor profile expected to be determined by the evolution of the Universe before dilution of the matter fields by cosmic expansion. Eventually, a simple analysis is performed in the bulk showing no obvious instability around the background solution. A full stability analysis taking into account brane bending modes is nevertheless necessary and left for future work.

A NON-SINGULAR CLOSED BOUNCING UNIVERSE WITHOUT VIOLATION OF NULL ENERGY CONDITION

A matter bouncing entropy-corrected cosmological model has been suggested. The model allows only positive curvature with negative pressure and no violation of the null energy condition. The result obtained in this paper is supported by some recent theoretical works where the combination of positive spatial curvature and vacuum energy leads to non-singular bounces with no violation of the null energy condition. An important feature of the current model is that evolutions of the cosmic pressure, energy density and equation of state parameter are independent of the values of the prefactors α and β in the corrected entropy-area relation. The validity of the classical and the new nonlinear energy conditions has been discussed. The cosmographic parameters have been analyzed.

The energy budget of cosmological first-order phase transitions beyond the bag equation of state

The stochastic gravitational-wave backgrounds (SGWBs) from the cosmological first-order phase transitions (FOPTs) serve as a promising probe for the new physics beyond the standard model of particle physics. When most of the bubble walls collide with each other long after they had reached the terminal wall velocity, the dominated contribution to the SGWBs comes from the sound waves characterized by the efficiency factor of inserting the released vacuum energy into the bulk fluid motions. However, the previous works of estimating this efficiency factor have only considered the simplified case of the constant sound velocities in both symmetric and broken phases, either for the bag model with equal sound velocities or ν-model with different sound velocities in the symmetric and broken phases, which is unrealistic from a viewpoint of particle physics. In this paper, we propose to solve the fluid EoM with an iteration method when taking into account the sound-velocity variation across the bubble wall for a general and realistic equation of state (EoS) beyond the simple bag model and ν-model. We have found a suppression effect for the efficiency factor of bulk fluid motions, though such a suppression effect could be negligible for the strong FOPT, in which case the previous estimation from a bag EoS on the efficiency factor of bulk fluid motions still works as a good approximation.

An Approach For Unity Field Theory With New Quantumvacuum Energy Aether Concept

Theories of relativity and quantum physics are basing on some complex abstract mathematical formalism which can be quite confusing and not always satisfactory concerning the interpretation of observed corresponding physical effects. For a revised approach of them, we present a new quantum vacuum energy Aether concept we will discuss qualitatively avoiding some abstract mathematical formalism often far from intuitive physical common sense. This is essentially concerning: the relative velocity of light and the Aether disprove, the particle/wave duality, the single particle interference quantum phenomena, the generalized confusion between absolute quantum determinism and undetermined probabilistic measurements of quantum states and the paradoxical possibility for a same quantum system to have at same time different states. Notwithstanding different suggested flaws about the principle of energy and impulse conservation and concerning the optical doppler effect and the postulate of an absolute light speed limit which is contradicted with some observation of superluminal particle transportation velocity. Paradoxical aspects of both theories of the quantum mechanics and theory of relativity are suggested to be sorted out with the rehabilitation of an absolute space reference and a newly defined Aether concept, basing on the equivalence between density of mass and density of quantum vacuum energy. Different aspects of the Field Theory and wave /mass /electric particles interactions are suggested to be interpreted in terms of Aether hydrodynamical energy displacement, fluctuation and waves. Electric charge and mass of particles and their kinetic energy are described in terms of energy of an associated Aether 3D transversal and/or longitudinal wave-packet moving with its group velocity in form of Aether vortices. This model is expected to sort out contradiction about different quantum phenomena and to open the way for new description and interpretation of corresponding new experimental results.

Vacuum densities and the Casimir forces for branes orthogonal to the AdS boundary

For a massive scalar field with general curvature coupling we evaluate the Wightman function in the geometry of two parallel branes perpendicular to the AdS boundary. On the separate branes, the field operator is constrained by Robin boundary conditions, in general, with different coefficients. In the region between the branes their contribution to the Wightman function is explicitly separated. By using this decomposition, the brane-induced effects on the vacuum expectation values (VEVs) for the field squared and energy-momentum tensor are investigated. The behavior of those expectation values is studied in various asymptotic regions of the parameters. The vacuum energy-momentum tensor in addition to the diagonal components has a nonzero off-diagonal stress. Depending on the boundary conditions and also on the distance from the branes, the vacuum energy density can be either positive or negative. The Casimir forces acting on the branes have two components. The first one corresponds to the standard normal force and the second one is parallel to the branes and presents the vacuum shear force. Unlike to the problem of parallel plates in the Minkowski bulk, the normal Casimir forces acting on separate branes differ if the boundary conditions on the branes are different. They can be either repulsive or attractive. In a similar way, depending on the coefficients in the boundary conditions, the shear force is directed toward or from the AdS boundary. The separate components may also change their signs as functions of the interbrane separation. At large proper separations between the branes, compared to the AdS curvature radius, both the components of the Casimir forces exhibit a power-law decay. For a massive scalar field this behavior is in contrast to that for the Minkowski bulk, where the decrease is exponential.

Study on the source of raw material and firing technique of glazed tiles bodies in the Ming Imperial palace site, Nanjing, China

AbstractThis article considered glazed tiles excavated from the Ming Imperial Palace site in Nanjing as the research object. Glazed tiles were selected and analyzed via vacuum porosimeter, thermal dilation (TD), X‐ray diffraction (XRD), and energy dispersive X‐ray fluorescence (EDXRF) to determine their physical property, firing temperature, phase composition, and chemical composition, respectively. Results show that the firing temperature of body belongs to the temperature range (of 950–1,100°C), whereas the water absorption and apparent porosity are large. The phase composition of glazed tile bodies is the same (predominantly quartz and mullite). However, some samples contain trace amounts of rutile, hematite, sodalite, and orthoclase. The firing temperature combined with the phase composition indicates that the raw material and firing process of glazed tile body samples have similarities, which embody of the strict and unified management system of the official kiln. The raw materials of glazed tile body in the Ming Imperial Palace site may come from Dangtu glazed kiln, whereas the rest of the samples remains to be explored. This study provides a scientific basis for understanding the evolution of glazed tile‐making technology in ancient China, and is important for the protection and repair of glazed buildings in the Ming Dynasty.