Negative Energy Density Research Articles

Higgs vacuum (in)stability during inflation. The dangerous relevance of de Sitter departure and Planck-suppressed operators

The measured Standard Model parameters lie in a range such that the Higgs potential, once extrapolated up to high scales, develops a minimum of negative energy density. This has important cosmological implications. In particular, during inflation, quantum fluctuations could have pushed the Higgs field beyond its potential barrier, triggering the formation of anti-de Sitter regions, with fatal consequences for our universe. By requiring that this did not happen, one can in principle connect (and constrain) Standard Model parameters with the energy scale of inflation. In this context, we highlight the sensitivity of the fate of our vacuum to seemingly irrelevant physics. In particular, the departure of inflation from an exact de Sitter phase, as well as Planck-suppressed derivative operators, can, already and surprisingly, play a decisive role in (de)stabilizing the Higgs during inflation. Furthermore, in the stochastic dynamics, we quantify the impact of the amplitude of the noise differing from the one of a massless field, as well as of going beyond the slow-roll approximation by using a phase-space approach. On a general ground, our analysis shows that relating the period of inflation to precision particle physics requires a knowledge of these “irrelevant” effects.

String clouds and radiation flows as sources of gravity in static or rotating cylinders

Static and stationary cylindrically symmetric space-times in general relativity are considered, supported by distributions of cosmic strings stretched in the azimuthal ([Formula: see text]), longitudinal ([Formula: see text]) or radial ([Formula: see text]) directions or and by pairs of mutually opposite radiation flows in any of these directions. For such systems, exact solutions are obtained and briefly discussed, except for radial strings (a stationary solution for them is not found); it is shown that static solutions with [Formula: see text]- and [Formula: see text]-directed radiation flows do not exist while for [Formula: see text]-directed strings a solution is only possible with negative energy density. Almost all solutions under discussion contain singularities, and all stationary solutions have regions with closed timelike curves, hence, most probably, only their well-behaved regions admit application to real physical situations.

Constraints on a special running vacuum model

We study a special running vacuum model (RVM) with Lambda = 3 alpha H^2+3beta H_0^4 H^{-2}+Lambda _0, where alpha , beta and Lambda _0 are the model parameters and H is the Hubble one. This RVM has non-analytic background solutions for the energy densities of matter and radiation, which can only be evaluated numerically. From the analysis of the CMB power spectrum and baryon acoustic oscillation along with the prior of alpha >0 to avoid having a negative dark energy density, we find that alpha <2.83times 10^{-4} and beta =(-0.2^{+3.9}_{-4.5})times 10^{-4} (95% C.L.). We show that the RVM fits the cosmological data comparably to the Lambda hbox {CDM}. In addition, we relate the fluctuation amplitude sigma _8 to the neutrino mass sum Sigma m_nu .

Charged gravastars with conformal motion in $f(R,T)$ gravity

This paper studies the effects of charge on a peculiar stellar object, recognized as gravastar, under the influence of $f(R,T)$ gravity by considering the conjecture of Mazur and Mottola in general relativity. The gravastar is also known as an alternative to a black hole and is expressed by three distinct domains named as (i) the interior domain, (ii) the intermediate shell and (iii) the exterior domain. We analyze these domains for a specific $f(R,T)$ gravity model conceding the conformal Killing vectors. In the interior domain, we assume that pressure is equal to negative energy density which leads to the existence of repulsive force on the spherical shell. The intermediate shell consists of ultra-relativistic plasma and pressure which shows a direct relation with energy density and counterbalances the repulsive force applied by the interior domain. The exterior vacuum spherical domain is taken to be the de Sitter spacetime illustrated by the Reissner-Nordstr\"{o}m metric. We conclude that non-singular solutions of charged gravastar with various physical properties such as length, energy, entropy and equation of state parameter are physically consistent.

Regular Bouncing Solutions, Energy Conditions, and the Brans—Dicke Theory

In general, to avoid a singularity in cosmological models involves the introduction of exotic kind of matter fields, for example, a scalar field with negative energy density. In order to have a bouncing solution in classical General Relativity, violation of the energy conditions is required. In this work, we discuss a case of the bouncing solution in the Brans-Dicke theory with radiative fluid that obeys the energy conditions, and with no ghosts.

New exact traversable wormhole solution to the Einstein-scalar-Gauss-Bonnet equations coupled to power-Maxwell electrodynamics

We present a novel, exact, traversable wormhole (T-WH) solution for $(3+1)$-dimensional Einstein-scalar-Gauss-Bonnet theory (EsGB) coupled to a power-Maxwell nonlinear electrodynamics (NLED). The solution is characterized by two parameters, $\mathcal{Q}\!_{\rm e}$ and $\mathcal{Q}\!_{_{ \mathcal{S} }}$, associated respectively with the electromagnetic field and the scalar field. We show that for $\mathcal{Q}^2_{\rm e} - \mathcal{Q}\!_{_{ \mathcal{S} }}>0$ the solution can be interpreted as a traversable wormhole. In the general case, with non-vanishing electromagnetic field, the scalar-Gauss-Bonnet term (sGB) is the only responsible for the negative energy density necessary for the traversability. In the limiting case of vanishing electromagnetic field, the scalar field becomes a phantom one keeping the WH throat open and in this case the Ellis WH solution \cite{Ellis} is recovered.

Testing a Quantum Inequality with a Meta-analysis of Data for Squeezed Light

In quantum field theory, coherent states can be created that have negative energy density, meaning it is below that of empty space, the free quantum vacuum. If no restrictions existed regarding the concentration and permanence of negative energy regions, it might, for example, be possible to produce exotic phenomena such as Lorentzian transversable wormholes, warp drives, time machines, violations of the second law of thermodynamics, and naked singularities. Quantum Inequalities (QIs) have been proposed that restrict the size and duration of the regions of negative quantum vacuum energy that can be accessed by observers. However, QIs generally are derived for situations in cosmology and are very difficult to test. Direct measurement of vacuum energy is difficult and to date no QI has been tested experimentally. We test a proposed QI for squeezed light by a meta-analysis of published data obtained from experiments with optical parametric amplifiers (OPA) and balanced homodyne detection. Over that last three decades, researchers in quantum optics have been trying to maximize the squeezing of light and the quantum vacuum and have succeeded in reducing the variance in the quantum vacuum fluctuations to -15 dB. To apply the QI, a time sampling function is required. In our meta-analysis different time sampling functions for the QI were examined, but in all physically reasonable cases the QI is violated by much or all of the measured data. This brings into question the basis for QI. Possible explanations are given for this surprising result.

Positivity enhancements to the Pn transport equations

One of the common methods for solving the radiation transport equation is to use a polynomial expansion for the angle variable(s). While each solution technique has its disadvantages, in some instances this method can result in oscillations large enough to give a negative radiation energy density, which is nonphysical. Some authors have recast the closure of the transport equations to guarantee positivity. Unfortunately, this results in messy nonlinear equations. Other authors post process each time step’s solution to improve positivity. In this work, the Pn equations are modified to be more diffusive, less oscillatory, more positive, and more accurate. No new solution techniques are required, just the scaling of some terms with constant factors and the addition of constant filter opacities; therefore, the solutions are still linear. This new solution method is called stretched and filtered Pn. Test problems are presented in one and two dimensions. Comparisons to the Dn and TPn closures are made in one dimension. Modifications to Dn and TPn are suggested.

Skyrmion clusters and conical droplets in bulk helimagnets with cubic anisotropy

Recent experimental findings in the bulk cubic helimagnet and Mott insulator ${\mathrm{Cu}}_{2}{\mathrm{OSeO}}_{3}$ highlight the paramount role of cubic anisotropy in stabilizing novel chiral and skyrmion phases. It was indeed found that if a magnetic field is applied along the easy $\ensuremath{\langle}001\ensuremath{\rangle}$ crystallographic direction, competing cubic and exchange anisotropies tilt the wave vector of the conical spiral away from the magnetic field [Qian et al., Sci. Adv. 4, eaat7323 (2018)]. Furthermore, in this configuration skyrmions have been observed in a broad range of temperatures and magnetic fields [Chacon et al., Nat. Phys. 14, 936 (2018)]. Starting from these experimental observations and on the basis of a phenomenological Dzyaloshinskii theory, we investigate additional implications of the cubic anisotropy for this specified field direction. By including cubic anisotropy we show that the phase transition between the conical and field-polarized or homogeneous states becomes first order. Furthermore, we show that this transition is accompanied by the formation of conical droplets---domains of the conical phase in the homogeneous state. We investigate the internal structure of these droplets, which at their boundaries encompass alternating regions of positive and negative energy densities with respect to the homogeneous state. We thus deduce that these droplets may be zipped and unzipped in phase during the first-order phase transition that occurs by either increasing or decreasing the magnetic field. On the other hand, we show that in the conical phase skyrmions may form clusters due to their attractive mutual interaction. However, in the homogeneous state, the skyrmion-skyrmion interaction becomes repulsive, and the skyrmion clusters expand and disperse isolated skyrmions. This mutual skyrmion repulsion prevents the stabilization of skyrmion clusters even if the energy of isolated skyrmions is lower than that of the homogeneous state. Yet this skyrmion dispersal may be prevented if skyrmions are surrounded by the circular spiral state and form skyrmion bags. Such a scenario could explain the existence of skyrmions in the field-polarized state reported experimentally.

Constraints on generalized Eddington-inspired Born-Infeld branes

The Palatini $f(|\hat{\Omega}|)$ gravity is a generalized theory of the Eddington-inspired Born-Infeld gravity, where $\Omega_{~N}^{K}\equiv\delta_{~N}^{K}+bg^{KL}R_{LN}(\Gamma)$ is an auxiliary tensor constructed with the spacetime metric $g$ and independent connection $\Gamma$. In this paper, we study $f(|\hat{\Omega}|)$ theory with $f(|\hat{\Omega}|)=|\hat{\Omega}|^{\frac{1}{2}+n}$ in the thick brane scenario and give some constraints on the brane model. We finally found an analytic solution of the thick brane generated by a single scalar field. The behavior of the negative energy density denotes the localization of the thick brane at the origin of the extra dimension. In our braneworld, the warp factor is divergent at the boundary of the extra dimension while the brane system is asymptotically anti$-$de Sitter. It is shown that the tensor perturbation of the brane is stable and the massless graviton is localized on the thick brane. Therefore, the effective Einstein-Hilbert action on the brane can be rebuilt in the low-energy approximation. According to the recent test of the gravitational inverse-square law, we give some constraints on the $f(|\hat{\Omega}|)$ brane.

Subvacuum effects on light propagation

Subvacuum effects arise in quantum field theory when a classically positive quantity, such as the local energy density, acquires a negative renormalized expectation value. Here we investigate the case of states of the quantized electromagnetic field with negative mean-squared electric field, and their effects on the propagation of light pulses in a nonlinear dielectric material with a nonzero third-order susceptibility. We identify two distinct signatures of the subvacuum effect in this situation. The first is an increase in the speed of the pulse, which is analogous to the superluminal light propagation in gravity which can arise from negative energy density. This increase in speed leads to a phase shift which might be large enough to observe. The second effect is a change in the frequency and power spectra of the pulse. We identify a specific measure of the modified spectra which can signal the presence of a negative mean squared electric field. These ideas are implemented in the particular example of a wave guide filled with a nonlinear dielectric material.

Supersymmetry breaking and ghost Goldstino in modulated vacua

We discuss spontaneous supersymmetry (SUSY) breaking mechanisms by means of modulated vacua in four-dimensional ${\cal N} =1$ supersymmetric field theories. The SUSY breaking due to spatially modulated vacua is extended to the cases of temporally and lightlike modulated vacua, using a higher-derivative model with a chiral superfield, free from the Ostrogradsky instability and the auxiliary field problem. For all the kinds of modulated vacua, SUSY is spontaneously broken and the fermion in the chiral superfield becomes a Goldstino. We further investigate the stability of the modulated vacua. The vacua are (meta)stable if the vacuum energy density is non-negative. However, the vacua become unstable due to the presence of the ghost Goldstino if the vacuum energy density is negative. Finally, we derive the relation between the presence of the ghost Goldstino and the negative vacuum energy density in the modulated vacua using the SUSY algebra.

Holography of negative energy states

Quantum states with negative energy densities have been long known to exist in quantum field theories. We explore the structure of such states for holographic theories using quantum information theory tools and show how certain negative energy states are naturally captured by the thermodynamics of black holes with hyperbolic horizon at zero temperature, suggesting that they provide a dual description of those states. Our results give a satisfying field theory understanding of the distinct thermodynamics of such black holes.

Rainbow Gravity: Big Bounce in Bianchi Type I Universe

We will examine the Bianchi Type I universe under the Rainbow Gravity formalism and calculate various quantities like the dynamical equation for the energy density and the negative energy density. Finally, we apply the analysis to a specific Rainbow Gravity model.

Was There a Negative Vacuum Energy in Your Past?

We introduce a novel model for the origin of the observable universe in which a flat universe with a positive vacuum energy is proceeded by a flat universe with a negative vacuum energy. A negative vacuum energy is consistent with a supersymmetric ground state similar to that predicted by superstring theories. A positive vacuum energy could emerge as a result of the gravitational collapse of the negative vacuum energy universe when the matter temperature reaches a characteristic value where supersymmetry is strongly broken. In principle this allows one to derive all the features of our expanding universe from a single parameter: the magnitude of the pre-big bang negative vacuum energy density. In this paper, a simple model for the big bang is introduced which allows us to use the present day entropy density, and temperature fluctuations of the CMB, together with the present day density of dark matter, to predict the magnitude of the negative vacuum energy. This model for the big bang also makes a dramatic prediction: dark matter consists of compact objects with masses on the order of 104 solar masses. Remarkably this is consistent with numerical simulations for how the primordial fluctuations in the density of dark matter give rise to the observed inhomogeneous distribution of matter in our universe. Our model for the big bang also allows for the production of some compact objects with masses greater than 104 solar masses which are consistent with observations of massive compact objects at the center of the earliest galaxies.

The Smeared Null Energy Condition

We propose a new bound on a weighted average of the null energy along a finite portion of a null geodesic: the Smeared Null Energy Condition (SNEC). We believe our bound is valid on scales small compared to the radius of curvature in any quantum field theory that is consistently coupled to gravity. If correct, our bound implies that regions of negative energy density are never strongly gravitating, and that isolated regions of negative energy are forbidden.

Unruh-DeWitt detectors as mirrors: Dynamical reflectivity and Casimir effect

We demonstrate that the Unruh-DeWitt harmonic-oscillator detectors in (1+1) dimensions derivative-coupled with a massless scalar field can mimic the atom mirrors in free space. Without introducing the Dirichlet boundary condition to the field, the reflectivity of our detector/atom mirror is dynamically determined by the interaction of the detector's internal oscillator and the field. When the oscillator-field coupling is strong, a broad frequency range of the quantum field can be mostly reflected by the detector mirror at late times. Constructing a cavity model with two such detector mirrors, we can see how the quantum field inside the cavity evolves from a continuous to a quasi-discrete spectrum which gives a negative Casimir energy density at late times. In our numerical calculations, the Casimir energy density in the cavity does not converge until the UV cutoff is sufficiently large, with which the two internal oscillators are always separable.

Teleparallel energy–momentum distribution of various black hole and wormhole metrics

Using the Einstein, Bergmann–Thomson (BT) and Landau–Lifshitz (LL) energy and momentum formulations in teleparallel gravity (TG), we obtain the total energy and momentum distributions for phantom black hole metric. We get different energy distributions similar to the earlier study and the momentum distributions vanish for phantom black hole metric in TG. These momentum solutions agree with the study of Sahoo et al. in general relativity. However, using Einstein, Bergmann–Thomson and Landau–Lifshitz energy and momentum complexes, we investigate regular black hole, asymptotically flat wormhole, anti-de Sitter wormhole and Ellis wormhole solutions in TG. We obtain (i) same BT and LL energy density solutions for regular black hole metric, (ii) same and zero energy distribution for asymptotically flat wormhole, (iii) proportion with Einstein and BT energy density solutions for anti-de Sitter wormhole, (iv) same and negative Einstein and BT energy density solutions for Ellis wormhole in TG.

Pentacoordinated, square pyramidal cationic PCP Ni(II) pincer complexes: ELF and QTAIM topological analyses of nickel–triflate interactions

A previous report introduced a new series of cationic nickel(II) complexes ligated by PCP-type pincer ligands featuring a charge-bearing imidazoliophosphine binding moiety and described their catalytic reactivities in hydroamination of nitriles into amidines. Solid-state characterization of the cationic acetonitrile adducts [(R-PIMIOCOP+)Ni(NCMe)(triflate)]+ (R-PIMIOCOP+ = κP,κC,κP-{2-(R2PO),6-(R2PC4H5N2)C6H3}; R = i-Pr, [1]+; Ph, [2]+) carried out in this follow-up study showed a distorted square pyramidal geometry and a Ni–triflate distance that was shorter than the sum of the Ni and O van der Waals radii, features suggestive of an unusual pentacoordination at the Ni(II) center. In contrast, the related aquo adduct [(i-Pr-PIMIOCOP+)Ni(OH2)(triflate)]+, [3]+, displayed a more conventional square planar geometry. Detailed structural comparisons and theoretical analyses conducted on these and related compounds have allowed a thorough examination of the Ni–triflate interactions in this family of complexes. Thus, topological analysis of the electron localization function (ELF) and quantum theory of atoms in molecules (QTAIM) showed that the Ni–triflate interaction is mostly ionic in nature, but has a weak covalence degree. The monosynaptic V(Ni) subvalence basin of nickel is indeed the ELF signature of the covalence degree of the ionic Ni–O bond, which can be quantified by the negative QTAIM energy density at the Ni–O bond critical point and by the absolute value of the ELF covariance 〈σ2(V(O), C(Ni))〉. The ionic character of the Ni–O bond is also reflected in an energy decomposition analysis, showing that this interaction is mostly electrostatic in nature. The computational analyses carried out on this family of complexes provide valuable insight into the character and relative strengths of various Ni–ligand interactions, and allow a number of useful conclusions, including the following: (1) significant Ni–anion interactions at the apical site are observed only with pincer-type ligands featuring at least one cationic imidazoliophosphine binding moiety; (2) these primarily electrostatic Ni–O interactions gain increasing covalence degree when different pincer backbone, co-ligand L, or counter-anions are introduced to enhance the electron deficiency of the Ni(II) center.

Short is strong: experimental electron density in a very short N···I halogen bond

Abstract2,3,5,6-Tetrafluoro-1,4-diiodobenzene and 4-(dimethylamino)pyridine co-crystallize in 1:2 stoichiometry. A diffraction experiment at standard resolution was already conducted in 2010 and revealed one of the shortest N···I contacts ever reported. We collected X-ray intensities at 100 K up to a very high resolution of 1.23 Å−1. These experimental data allowed to refine a structure model based on atom-centered multipoles according to the Hansen-Coppens approach and provided an experimental electron density. A subsequent analysis with the help of Bader’s atoms in molecules theory showed a strong interaction between the pyridine N atom and theσhole of its closest iodine neighbor on the halogenated benzene. This contact is characterized by a distance of 2.6622(4) Å and associated with a remarkably large electron density of 0.359(5)e⋅Å−3in the (3, −1) critical point, unprecedented for a secondary interaction. This bona fide shortest halogen bond ever investigated by an experimental charge density study is associated with a significantly negative total energy density in the bond critical point and thus can reliably be classified as strong. Both the electron density and the position of the bond critical point suggest to compare the short N···I contact to coordinative or covalent bonds rather than toσhole interactions.