Vacuum Energy Research Articles

Newtonian Cosmology and Evolution of κ-Deformed Universe

Considering space-time to be non-commutative, we study the evolution of the universe employing the approach of Newtonian cosmology. Generalizing the conservation of energy and the first law of thermodynamics to κ-deformed space-time, we derive the modified Friedmann equations, valid up to the first order, in the deformation parameter. Analyzing these deformed equations, we derive the time evolution of the scale factor in cases of radiation-dominated, matter-dominated, and vacuum (energy)-dominated universes. We show that the rate of change of the scale factor in all three situations is modified by the non-commutativity of space-time, and this rate depends on the sign of the deformation parameter, indicating a possible explanation for the observed Hubble tension. We undertake this investigation for two different realizations of non-commutative space-time coordinates. In both cases, we also argue for the existence of bounce in the evolution of the universe.

On the inevitable lightness of vacuum

In this essay, we present a new understanding of the cosmological constant problem, built upon the realization that the vacuum energy density can be expressed in terms of a phase space volume. We introduce a UV-IR regularization which implies a relationship between the vacuum energy and entropy. Combining this insight with the holographic bound on entropy then yields a bound on the cosmological constant consistent with observations. It follows that the universe is large, and the cosmological constant is naturally small, because the universe is filled with a large number of degrees of freedom.

Running vacuum in QFT in FLRW spacetime: the dynamics of rho _{textrm{vac}}(H) from the quantized matter fields

Phenomenological work in the last few years has provided significant support to the idea that the vacuum energy density (VED) is a running quantity with the cosmological evolution and that this running helps to alleviate the cosmological tensions afflicting the Lambda CDM. On the theoretical side, recent devoted studies have shown that the properly renormalized rho _{textrm{vac}} in QFT in FLRW spacetime adopts the ‘running vacuum model’ (RVM) form. While in three previous studies by two of us (CMP and JSP) such computations focused solely on scalar fields non-minimally coupled to gravity, in the present work we compute the spin-1/2 fermionic contributions and combine them both. The calculation is performed using a new version of the adiabatic renormalization procedure based on subtracting the UV divergences at an off-shell renormalization point M. The quantum scaling of rho _{textrm{vac}} with M turns into cosmic evolution with the Hubble rate, H. As a result the ‘cosmological constant’ Lambda appears in our framework as the nearly sustained value of 8pi G(H)rho _{textrm{vac}}(H) around (any) given epoch H, where G(H) is the gravitational coupling, which is also running, although very mildly (logarithmically). We find that the VED evolution at present reads delta rho _textrm{vac}(H)sim nu _{textrm{eff}}, m_{textrm{Pl}}^2 left( H^2-H_0^2 right) (|nu _{textrm{eff}}|ll 1). The coefficient nu _{textrm{eff}} receives contributions from all the quantized fields, bosons and fermions, which we compute here for an arbitrary number of matter fields. Remarkably, there also exist higher powers mathcal{O}(H^{6}) which can trigger inflation in the early universe. Finally, the equation of state (EoS) of the vacuum receives also quantum corrections from bosons and fermion fields, shifting its value from − 1. The striking consequence is that the EoS of the quantum vacuum may nowadays effectively appears as quintessence.

Comment on the Vacuum Energy Density for λϕ4 Theory in d Spacetime Dimensions

In a recent article we showed that the vacuum energy density in two spacetime dimensions for a wide variety of integrable quantum field theories has the form ρvac=−m2/2g where m is a physical mass and g is a generalized coupling, where in the free field limit g→0, ρvac diverges. This vacuum energy density has the form ⟨Tμν⟩=−ρvacgμν, and has previously been considered as a contribution to the stress energy tensor in Einstein’s gravity as a “cosmological constant”. We speculated that in four spacetime dimensions ρvac takes a similar form ρvac=−m4/2g, but did not support this idea in any specific model. In this article, we study this problem for λϕ4 theory in d spacetime dimensions. We show how to obtain the exactρvac for the sinh–Gordon theory in the weak coupling limit by using a saddle point approximation. This calculation indicates that the vacuum energy can be well-defined, positive or negative, without spontaneous symmetry breaking. We also show that ρvac satisfies a Callan–Symanzik type of renormalization group equation. For the most interesting case physically, ρvac is positive and can arise from a marginally relevant negative coupling g and the vacuum energy flows to zero at low energies.

Probing dark fluids and modified gravity with gravitational lensing

ABSTRACT We generalize the result of Rindler-Ishak for the lensing deflection angle in a Schwarzschild–deSitter (SdS) space–time, to the case of a general spherically symmetric fluid beyond the cosmological constant. We thus derive an analytic expression to first post-Newtonian order for the lensing deflection angle in a general static spherically symmetric metric of the form $\mathrm{ d}s^2 = f(r)\mathrm{ d}t^{2} -\frac{\mathrm{ d}r^{2}}{f(r)}-r^{2}(\mathrm{ d}\theta ^2 +\sin ^2 \theta \mathrm{ d}\phi ^2)$ with $f(r) = 1 - \frac{2m}{r}-\sum _{i} b_\mathrm{ i}\,\, r_0^{-q_i}\,\, \left(\frac{r_0}{r}\right)^{q_i}$, where r0 is the lensing impact parameter, $b_i\ll r_0^{q_i}$, m is the mass of the lens, and qi are real arbitrary constants related to the properties of the fluid that surrounds the lens or to modified gravity. This is a generalization of the well known Kiselev black hole metric. The approximate analytic expression of the deflection angle is verified by an exact numerical derivation and in special cases it reduces to results of previous studies. The density and pressure of the spherically symmetric fluid that induces this metric is derived in terms of the constants bi. The Kiselev case of a Schwarzschild metric perturbed by a general spherically symmetric dark fluid (e.g. vacuum energy) is studied in some detail and consistency with the special case of Rindler-Ishak result is found for the case of a cosmological constant background. Observational data of the Einstein radii from distant clusters of galaxies lead to observational constraints on the constants bi and through them on the density and pressure of dark fluids, field theories, or modified gravity theories that could induce this metric.

Quantum trans-Planckian physics inside black holes and its spectrum

We provide a quantum unifying picture for black holes of all masses and their main properties covering classical, semiclassical, Planckian, and trans-Planckian gravity domains: space-time, size, mass, vacuum (``zero-point'') energy, temperature, partition function, density of states, and entropy. Novel results of this paper are that black hole interiors are always quantum, trans-Planckian, and of constant curvature. This is so for all black holes, including the most macroscopic and astrophysical ones. The black hole interior trans-Planckian vacuum is similar to the earliest cosmological vacuum, where the classical gravity dual is the low energy gravity vacuum---today, dark energy. There is no singularity boundary at $r=0$; the quantum space-time is regular. We display the quantum Penrose diagram of the Schwarzschild-Kruskal black hole. The complete black hole instanton (imaginary time) covers the known classical Gibbons-Hawking instanton plus a new, central, highly dense quantum core of Planck length radius and constant curvature. The complete partition function, entropy, temperature, decay rate, discrete levels, and density of states all include the trans-Planckian domain. The semiclassical black hole entropy (the Bekenstein-Hawking entropy) $(\sqrt{n}{)}^{2}$ ``interpolates'' between the quantum point particle entropy ($n$) and the quantum string entropy $\sqrt{n}$, while the quantum trans-Planckian entropy is $1/(\sqrt{n}{)}^{2}$. Black hole evaporation finishes in a pure (nonmixed) quantum state of particles, gravitons, and radiation.

Vacuum energy density and gravitational entropy

The failure to calculate the vacuum energy is a central problem in theoretical physics. Presumably the problem arises from the insistent use of effective field theory reasoning in a context that is well beyond its intended scope. If one follows this path, then one is led inevitably to statistical or anthropic reasoning for observations. It appears that a more palatable resolution of the vacuum energy problem requires some form of UV/IR feedback. In this paper we take the point of view that such feedback can be thought of as arising by defining a notion of quantum space-time. We reformulate the regularized computation of vacuum energy in such a way that it can be interpreted in terms of a sum over elementary phase space volumes, that we identify with a ground state degeneracy. This observation yields a precise notion of UV/IR feedback, while leaving a scale unfixed. Here we argue that holography can be thought to provide a key piece of information: we show that equating this microscopic ground state degeneracy with macroscopic gravitational entropy yields a prediction for the vacuum energy that can easily be consistent with observations. Essentially, the smallness of the vacuum energy is tied to the large size of the Universe. We discuss how within this scenario notions of effective field theory can go so wrong.

Quantum entanglement of masses with nonlocal gravitational interaction

We examine the quantum gravitational entanglement of two test masses in the context of linearized General Relativity with specific non-local interaction with matter. To accomplish this, we consider an energy-momentum tensor describing two test particles of equal mass with each possessing some non-zero momentum. After discussing the quantization of the linearized theory, we compute the gravitational energy shift which is operator-valued in this case. As compared to the local gravitational interaction, we find that the change in the gravitational energy due to the self-interaction terms is finite. We then move on to study the quantum gravity induced entanglement of masses for two different scenarios. The first scenario involves treating the two test masses as harmonic oscillators with an interaction Hamiltonian given by the aforesaid gravitational energy shift. In the second scenario, each of the test masses is placed in a quantum spatial superposition of two locations, based on their respective spin states, and their entanglement being induced by the gravitational interaction and the shift in the vacuum energy. For these two scenarios, we compute both the concurrence and the von Neumann entropy; showing that an increase in the non-locality of the gravitational interaction results in a decrease in both of these quantities.

On de Sitter spacetime and string theory

We review various aspects of de Sitter spacetime in string theory: its status as an Effective Field Theory spacetime solution, its relation to the vacuum energy problem in string theory, its (global) holographic definition in terms of two entangled and noncanonical conformal field theories as well as a realization of a realistic de Sitter universe endowed with the observed visible matter and the necessary dark sector in order to reproduce the realistic cosmological structure. In particular, based on the new insight regarding the cosmological constant problem in string theory, we argue that in a doubled, [Formula: see text]-duality-symmetric, phase-space-like and noncommutative generalized-geometric formulation, string theory can naturally lead to a small and positive cosmological constant that is radiatively stable and technically natural. Such a formulation is fundamentally based on a quantum spacetime, but in an effective spacetime description of this general formulation of string theory, the curvature of the dual spacetime is the cosmological constant of the observed spacetime, while the size of the dual spacetime is the gravitational constant of the same observed spacetime. Also, the three scales associated with intrinsic noncommutativity of string theory, the cosmological constant scale, the Planck scale as well as the Higgs scale, can be arranged to satisfy various seesaw-like formulae. Along the way, we show that these new features of string theory can be implemented in a particular deformation of cosmic-string-like models.

A functional approach to the Van der Waals interaction

We evaluate the quantum interaction energy between two neutral atoms, using a functional integral approach. In our setup, each atom has an electron bound to the nucleus via a harmonic potential. The resulting expression for the vacuum energy becomes the Van der Waals interaction at the first non-trivial order in an expansion in powers of the fine structure constant, encompassing both the long and short distance behaviours. We also explore the opposite, strong-coupling limit, which yields a result for the interaction energy as well as a threshold for the existence of a vacuum decay probability, manifested here as an imaginary part for the effective action. In the weak-coupling limit, we also study the effect of using a general central potential for the internal structure of the atoms.

A Wheeler–DeWitt Quantum Approach to the Branch-Cut Gravitation with Ordering Parameters

In this contribution to the Festschrift for Prof. Remo Ruffini, we investigate a formulation of quantum gravity using the Hořava–Lifshitz theory of gravity, which is General Relativity augmented by counter-terms to render the theory regularized. We are then led to the Wheeler–DeWitt (WDW) equation combined with the classical concepts of the branch-cut gravitation, which contemplates as a new scenario for the origin of the Universe, a smooth transition region between the contraction and expansion phases. Through the introduction of an energy-dependent effective potential, which describes the space-time curvature associated with the embedding geometry and its coupling with the cosmological constant and matter fields, solutions of the WDW equation for the wave function of the Universe are obtained. The Lagrangian density is quantized through the standard procedure of raising the Hamiltonian, the helix-like complex scale factor of branched gravitation as well as the corresponding conjugate momentum to the category of quantum operators. Ambiguities in the ordering of the quantum operators are overcome with the introduction of a set of ordering factors α, whose values are restricted, to make contact with similar approaches, to the integers α=[0,1,2], allowing this way a broader class of solutions for the wave function of the Universe. In addition to a branched universe filled with underlying background vacuum energy, primordial matter and radiation, in order to connect with standard model calculations, we additionally supplement this formulation with baryon matter, dark matter and quintessence contributions. Finally, the boundary conditions for the wave function of the Universe are imposed by assuming the Bekenstein criterion. Our results indicate the consistency of a topological quantum leap, or alternatively a quantum tunneling, for the transition region of the early Universe in contrast to the classic branched cosmology view of a smooth transition.

Why there is something rather than nothing: A proposal for the cosmological constant problem

This work is based on the idea that the observed cosmological constant is preferred for a stable vacuum, where a running gravitational coupling is considered. The most probable value of the cosmological constant is determined by the minimum of the vacuum energy density, and it is just proportional to the matter density. When the cosmological constant is connected with a modified dispersion relation (MDR) via an effective Newton constant, it may impose a constraint on the latter: the exponent of the leading correction should be n = 3.

Running Vacuum in the Universe: Phenomenological Status in Light of the Latest Observations, and Its Impact on the σ8 and H0 Tensions

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

Time-symmetric quantization of relativistic fields. 1. Complex fields, massless gauge fields and gravitons

In the standard formulation of quantum field theory (QFT), where there are only positive energy particles and antiparticles, the energy and charge of the vacuum diverge, which, due to the existence of gravity, leads to the inconsistency of the theory (cosmological constant problem). In the article, it is shown that in the Stueckelberg-Feynman (SF) interpretation, where antiparticles are described as negative energy particles moving backward in time, the zero-point energy and zero-point charge of vacuum of complex fields are absent and there is no cosmological constant problem. However, until now it was believed that the SF interpretation leads to negative probabilities and incompatible with QFT. In the article, it is presented a new formulation of QFT on the basis of the SF interpretation in the form of time-symmetric quantization (TSQ), where the probability of states is positive. In TSQ, the consequences of the SF interpretation are taken into account consecutively and it is shown that: a) the negative sign of the norm of states only changes the sign of the wave function, and not the probabilities; b) the expression of backward in time integrals through the forward in time integrals changes sign; c) the time ordering of the operators is symmetric in time and writing them through the usual ordering leads to the standard diagram technique. For this reason, TSQ correctly describes the known observable effects. In TSQ, the results of unification models change, in particular, a) there is no zero-point energy even with broken supersymmetry between complex fields; b) there is no zero-point energy of modes in string theories, which allows to include gravity, but there is no a conformal anomaly and the dimension of space can be arbitrary.

The Emergent Entangled Informational Universe

The dream of capturing the workings of the entire universe in a single equation or a simple set of equations is still pursued. A set of five new equivalent formulations of entropy based on the introduction of the mass of the information bit in Louis de Broglie's hidden thermodynamics and on the physicality of information, is proposed, within the framework of the emergent entangled informational universe model, which is based on the principle of strong emergence, the mass-energy-information equivalence principle and the Landauer’s principle. This model can explain various process as informational quantum processes such energy, dark matter, dark energy, cosmological constant and vacuum energy. The dark energy is explained as a collective potential of all particles with their individual zero-point energy emerging from an informational field, distinct from the usual fields of matter of quantum field theory, associated with dark matter as having a finite and quantifiable mass; while resolving the black hole information paradox by calculating the entropy of the entangled Hawking radiation, and shedding light on gravitational fine-grained entropy of black holes. This model explains the collapse of the wave function by the fact that a measure informs the measurer about the system to be measured and, this model is able to invalidate the many worlds interpretation of quantum mechanics and the simulation hypothesis.

One-loop effective action and emergent gravity on quantum spaces in the IKKT matrix model

A detailed derivation of 3 + 1 dimensional induced or emergent gravity in the IKKT matrix model at one loop is given, as announced in [1]. The mechanism requires a brane configuration with structure {mathcal{M}}^{3,1}times mathcal{K}subset {mathbb{R}}^{9,1} , where {mathcal{M}}^{3,1} is the noncommutative space-time brane, and mathcal{K} are compact fuzzy extra dimensions embedded in target space. The 3+1-dimensional Einstein-Hilbert action then arises in the one loop effective action of the maximally supersymmetric IIB or IKKT matrix model, with effective Newton constant determined by the Kaluza-Klein scale of mathcal{K} . At weak coupling, all physical modes are confined to the brane, leading to 3 + 1-dimensional low-energy physics. The Einstein-Hilbert action can be interpreted as interaction of mathcal{K} with the space-time brane via IIB supergravity. The vacuum energy does not act as cosmological constant, but stabilizes the brane structure at one loop.

Emergent gravity from the IIB matrix model and cancellation of a cosmological constant

We review a cosmological model where the metric determinant plays a dynamical role and present new numerical results on the cancellation of the vacuum energy density including the contribution of a cosmological constant. The action of this model is only invariant under restricted coordinate transformations with unit Jacobian (the same restriction appears in the well-known unimodular-gravity approach to the cosmological constant problem). As to the possible origin of the nonstandard terms in the matter action of the model, we show that these terms can, in principle, arise from the emergent gravity in the IIB matrix model, a nonperturbative formulation of superstring theory.

Thermal decomposition of polypropylene plastics through vacuum pyrolysis

The technique of thermal pyrolysis has a great contribution to waste-to-energy platform and circular economic mission. This study used an internal heating process for the vacuum pyrolysis of plastic waste. Eight heating tubes were placed inside a reactor to accelerate heat transfer to the feedstock. Uniform temperature distribution was achieved in <1 h. After 90 min, three phases of pressure profiles were identified: decomposing samples, maximum feedstock cracking, and stability occurrences. Internal pressure decreased with the reduction of condensable gas. Pyrolytic oil was similar to conventional fuels (gasoline and diesel), with the percentage of lower hydrocarbons C5–C10 at 73%, C11–C22 at 18%, and >C22 at 9%. Gas chromatography–thermal conductivity detector analysis of noncondensable gases revealed that the main product of PP with 75% area was C2H6. Furthermore, the Taguchi method was used to optimize the vacuum pyrolysis of waste to energy. Optimal operating conditions for maximum pyrolytic yields were as follows: temperature 425 °C, heating rate 15 °C/min, residence time 6 h, and output flow rate 0.1 L/min. Moreover, the physical properties, cetane number, soot propensities, and auto-ignition temperature of pyrolytic oil were comparable to petroleum diesel. The heating value of the oil product was 55.96 MJ/kg, which was higher compared with petroleum fuels. Vacuum pyrolysis mass, carbon, and energy balances were also determined. This study demonstrated the novel use of internal heating in vacuum pyrolysis. Ultimately, this study provided a new technique of internal heating method in vacuum pyrolysis.

Electromagnetic vacuum stresses and energy fluxes induced by a cosmic string in de Sitter spacetime

For the electromagnetic field in [Formula: see text]-dimensional locally de Sitter (dS) spacetime, we analyze the effects of a generalized cosmic string type defect on the vacuum expectation value of the energy-momentum tensor. For the Bunch–Davies vacuum state, the topological contributions are explicitly extracted in both the diagonal and off-diagonal components. The latter describes the presence of radially directed energy flux in the vacuum state. It vanishes for [Formula: see text] because of the conformal invariance of the electromagnetic field and is directed towards the cosmic string for [Formula: see text]. The topological contributions in the vacuum stresses are anisotropic and, unlike the geometry of a cosmic string in the Minkowski spacetime, for [Formula: see text] the stresses along the directions parallel to the string core differ from the energy density. Depending on the planar angle deficit and the distance from the cosmic string, the corresponding expectation values can be either positive or negative. Near the cosmic string the effect of the gravitational field on the diagonal components of the topological part is weak and the leading terms in the respective expansions coincide with the expectation values for a cosmic string in the background of Minkowski spacetime. The spacetime curvature essentially modifies the behavior of the topological terms at proper distances from the cosmic string larger than the dS curvature radius. In that region, the topological contributions in the diagonal components of the energy–momentum tensor decay in inverse proportion to the fourth power of the proper distance and the energy flux density behaves as inverse-fifth power for all values of the spatial dimension [Formula: see text]. The exception is the energy density in the special case [Formula: see text]. For a cosmic string in the Minkowski bulk the energy flux is absent and the diagonal components are proportional to the [Formula: see text]th power of the inverse distance.

A quantum cosmology approach to cosmic coincidence and inflation

This work studies the quantum cosmology of a closed, spatially homogeneous, and isotropic FLRW minisuperspace model with electromagnetic radiation as a matter content. We solve the associated Wheeler-DeWitt (WDW) equation using the holographic regularization method and show that the electromagnetic zero-point energy forms the vacuum energy and provides a unified resolution to the horizon, flatness, singularity, and cosmic coincidence problems. This quantum cosmology approach composes an alternative to the usual inflationary paradigm and can be extended to more general matter contents and emergent gravity schemes.