Negative Energy Density Research Articles

Tetrel bonds between PhSiF3/PhTH3(T = Si, Ge, Sn) and H3ZO (Z = N, P, As): A pentacoordinate silicon (IV) complex

AbstractThe nature of the complexes PhTH3H3ZO and PhSiF3H3ZO (T = Si, Ge, and Sn; Z = N, P, and As) has been investigated at the MP2/aug’‐cc‐pVTZ(PP) level. These complexes are primarily stabilized by one T···O tetrel bond. Interaction energies of these complexes vary from 11 to 220 kJ/mol, and T···O separations from 1.89 to 3.09 Å. Charge transfer from the O lone pair into the CT and TH σ* antibonding orbitals leads to the stabilization of these complexes. The T···O tetrel bond between PhTH3/PhSiF3and H3NO exhibits a significant degree of covalence, characterized by the large interaction energy, negative energy density, and large charge transfer. Furthermore, a pentacoordinate silicon (IV) complex is formed in PhSiF3H3NO with the Si···O distance almost close to the length of SiO bond. This indicates that the oxygen atom in N‐oxides shows a strong affinity to the silicon atom in organosilicon compounds.

A time machine for free fall into the past

Inspired by some recent works of Tippett–Tsang and Mallary–Khanna–Price, we present a new spacetime model containing closed timelike curves (CTCs). This model is obtained postulating an ad hoc Lorentzian metric on , which differs from the Minkowski metric only inside a spacetime region bounded by two concentric tori. The resulting spacetime is topologically trivial, free of curvature singularities and is both time and space orientable; besides, the inner region enclosed by the smaller torus is flat and displays geodesic CTCs. Our model shares some similarities with the time machine of Ori and Soen but it has the advantage of a higher symmetry in the metric, allowing for the explicit computation of a class of geodesics. The most remarkable feature emerging from this computation is the presence of future-oriented timelike geodesics starting from a point in the outer Minkowskian region, moving to the inner spacetime region with CTCs, and then returning to the initial spatial position at an earlier time; this means that time travel to the past can be performed by free fall across our time machine. The amount of time travelled into the past is determined quantitatively; this amount can be made arbitrarily large keeping non-large the proper duration of the travel. An important drawback of the model is the violation of the classical energy conditions, a common feature of many time machines. Other problems emerge from our computations of the required (negative) energy densities and of the tidal accelerations; these are small only if the time machine is gigantic.

Implications of an extended dark energy cosmology with massive neutrinos for cosmological tensions

We perform a comprehensive analysis of the most common early- and late-Universe solutions to the $H_0$, Ly-$\alpha$, and $S_8$ discrepancies. When considered on their own, massive neutrinos provide a natural solution to the $S_8$ discrepancy at the expense of increasing the $H_0$ tension. If all extensions are considered simultaneously, the best-fit solution has a neutrino mass sum of $\sim 0.4$ eV, a dark energy equation of state close to that of a cosmological constant, and no additional relativistic degrees of freedom. However, the $H_0$ tension, while weakened, remains unresolved. Motivated by this result, we perform a non-parametric reconstruction of the evolution of the dark energy fluid density (allowing for negative energy densities), together with massive neutrinos. When all datasets are included, there exists a residual $\sim1.9\sigma$ tension with $H_0$. If this residual tension remains in the future, it will indicate that it is not possible to solve the $H_0$ tension solely with a modification of the late-Universe dynamics within standard general relativity. However, we do find that it is possible to resolve the tension if either galaxy BAO or JLA supernovae data are omitted. We find that \textit{negative} dark energy densities are favored near redshift $z\sim2.35$ when including the Ly-$\alpha$ BAO measurement (at $\sim 2\sigma$). This behavior may point to a negative curvature, but it is most likely indicative of systematics or at least an underestimated covariance matrix. Quite remarkably, we find that in the extended cosmologies considered in this work, the neutrino mass sum is always close to $0.4$ eV regardless of the choice of external datasets, as long as the $H_0$ tension is solved or significantly decreased.

Complete conformal classification of the Friedmann–Lemaître–Robertson–Walker solutions with a linear equation of state

We completely classify Friedmann–Lemaître–Robertson–Walker solutions with spatial curvature and equation of state , according to their conformal structure, singularities and trapping horizons. We do not assume any energy conditions and allow , thereby going beyond the usual well-known solutions. For each spatial curvature, there is an initial spacelike big-bang singularity for w > −1/3 and , while there is no big-bang singularity for w < −1 and . For K = 0 or −1, −1 < w < −1/3 and , there is an initial null big-bang singularity. For each spatial curvature, there is a final spacelike future big-rip singularity for w < −1 and , with null geodesics being future complete for but incomplete for w < −5/3. For w = −1/3, the expansion speed is constant. For −1 < w < −1/3 and K = 1, the universe contracts from infinity, then bounces and expands back to infinity. For K = 0, the past boundary consists of timelike infinity and a regular null hypersurface for −5/3 < w < −1, while it consists of past timelike and past null infinities for . For w < −1 and K = 1, the spacetime contracts from an initial spacelike past big-rip singularity, then bounces and blows up at a final spacelike future big-rip singularity. For w < −1 and K = −1, the past boundary consists of a regular null hypersurface. The trapping horizons are timelike, null and spacelike for , and , respectively. A negative energy density () is possible only for K = −1. In this case, for w > −1/3, the universe contracts from infinity, then bounces and expands to infinity; for −1 < w < −1/3, it starts from a big-bang singularity and contracts to a big-crunch singularity; for w < −1, it expands from a regular null hypersurface and contracts to another regular null hypersurface.

Reconstruction of the Dark Energy Equation of State from the Latest Observations

Abstract Since the discovery of the accelerating expansion of our universe in 1998, studying the features of dark energy has remained a hot topic in modern cosmology. In the literature, dark energy is usually described by w ≡ P/ρ, where P and ρ denote its pressure and energy density. Therefore, exploring the evolution of w is the key approach to understanding dark energy. In this work, we adopt three different methods, polynomial expansion, principal component analysis, and the correlated prior method, to reconstruct w with a collection of the latest observations, including the type-Ia supernova, cosmic microwave background, large-scale structure, Hubble measurements, and baryon acoustic oscillations (BAOs), and find that the concordance cosmological constant model (w = −1) is still safely consistent with these observational data at the 68% confidence level. However, when we add the high-redshift BAO measurement from the Lyα forest (Lyα FB) of BOSS DR11 quasars into the calculation, there is a significant impact on the reconstruction result. In the standard ΛCDM model, since the Lyα FB data slightly prefer a negative dark energy density, in order to avoid this problem, a dark energy model with a w significantly smaller than −1 is needed to explain this Lyα FB data. In this work, we find the consistent conclusion that there is a strong preference for the time-evolving behavior of dark energy w at high redshifts, when including the Lyα FB data. Therefore, we think that this Lyα FB data needs to be watched carefully attention when studying the evolution of the dark energy equation of state.

Fostering the Basic Instinct of Boron in Boron-Beryllium Interactions.

A set of complexes L2HB···BeX2 (L = CNH, CO, CS, N2, NH3, NCCH3, PH3, PF3, PMe3, OH2; X = H, F) containing a boron-beryllium bond is described at the M06-2X/6-311+G(3df,2pd)//M062-2X/6-31+G(d) level of theory. In this quite unusual bond, boron acts as a Lewis base and beryllium as a Lewis acid, reaching binding energies up to -283.3 kJ/mol ((H2O)2HB···BeF2). The stabilization of these complexes is possible thanks to the σ-donor role of the L ligands in the L2HB···BeX2 structures and the powerful acceptor nature of beryllium. According to the topology of the density, these B-Be interactions present positive laplacian values and negative energy densities, covering different degrees of electron sharing. ELF calculations allowed measuring the population in the interboundary B-Be region, which varies between 0.20 and 2.05 electrons upon switching from the weakest ((CS)2HB···BeH2) to the strongest complex ((H2O)2HB···BeF2). These B-Be interactions can be considered as beryllium bonds in most cases.

Modified Friedmann equations in braneworld scenario

Firstly we present a brief discussion about braneworld model and the derivation of Friedmann equations in the braneworld scenario. Next we carry out a dynamical analysis of the modified Friedmann equations. Lastly, we perform a numerical computation using the Metropolis-Hastings algorithm to compute several free parameters of the modified Friedmann equations. Among others, we found that the brane tension is not large enough to support a nucleosynthesis process which correctly reproduce the abundance of present light elements. Also, we found a negative dark-radiation energy density, and thus indicating a possibility of non-singular initial universe.

Nonlocal modified Einstein’s field equation and geometric origin of a small cosmological constant

We show that the description of the spacetime in terms of backward-forward extension of its corresponding metric leads to the geometric origin of a small cosmological constant. The nonlocal cosmological constant appears in the Einstein’s field equation and its mathematical expression depends on the nonlocal metric, Ricci scalar and the infinitesimal nonlocal parameter introduced in the theory. The modified theory has interesting consequences in FRW cosmology, mainly a nonsingular universe, the occurrence of a late-time accelerated expansion of the universe and an early universe dominated by a negative energy density and a positive pressure. Our model can explain the acceleration of the universe without a fine-tuned cosmological constant $\Lambda$ .

Theoretical and Practical Approach of Soft Template Synthesis for the Preparation of MnO2 Supercapacitor Electrode

Mesoporous manganese dioxide was successfully synthesized by alkene oxidation with permanganate in soft template medium. Four linear and three cyclic alkenes have been used as reactants to show their impact on the MnO2 particles microstructure (specially the pore volume), on their agglomeration, and hence on their electrochemical performances as positive electrode materials in supercapacitors. The reaction proceeds via an intermediate product step, a manganate(V) cyclic diester, capable of producing aggregates. Aggregate macromolecular characteristics, such as intrinsic viscosity [η], molecular weight M, aggregation number N, and radius R, depend on the alkene employed. The role of CTAP as phase-transfer agent and as templating agent for MnO2 synthesis when associated with alkene is also confirmed. This first study allowed the proposition of a structure for the aggregates (called model B in the text). The electrochemical performances of the manganese oxides were subsequently determined with aqueous, environmentally friendly K2SO4 electrolyte. Suitable performances, in terms of high specific capacitances (>150 F·g–1) are provided by oxides prepared by employing bulky cyclic or long-chain linear alkenes. Asymmetric devices AC∥MnO2 with one of the mesoporous manganese oxide as the positive electrode, obtained from the oxidation of 1-octadecene, and activated carbon (AC) as the negative electrode yield suitable energy density of 18.2 Wh·kg–1 and a power density of 0.2 kW·kg–1 for electrochemical capacitor purposes. Finally, this particular device, cycled under galvanostatic regimes, shows a high-capacitance retention (81.2% after 10000 cycles). Therefore, this particular soft template method is suitable for the preparation of supercapacitor electrodes.

Evolution of cyclic mixmaster universes with noncomoving radiation

We study a model of a cyclic, spatially homogeneous, anisotropic 'mixmaster' universe of Bianchi type IX, containing a radiation field with non-comoving ('tilted' with respect to the tetrad frame of reference) velocities and vorticity. We employ a combination of numerical and approximate analytic methods to investigate the consequences of the second law of thermodynamics on the evolution. We model a smooth cycle-to-cycle evolution of the mixmaster universe, bouncing at a finite minimum, by the device of adding a comoving 'ghost' field with negative energy density. In the absence of a cosmological constant, an increase in entropy, injected at the start of each cycle, causes an increase in the volume maxima, increasing approach to flatness, falling velocities and vorticities, and growing anisotropy at the expansion maxima of successive cycles. We find that the velocities oscillate rapidly as they evolve and change logarithmically in time relative to the expansion volume. When the conservation of momentum and angular momentum constraints are imposed, the spatial components of these velocities fall to smaller values when the entropy density increases, and vice versa. Isotropisation is found to occur when a positive cosmological constant is added because the sequence of oscillations ends and the dynamics expand forever, evolving towards a quasi de Sitter asymptote with constant velocity amplitudes. The case of a single cycle of evolution with a negative cosmological constant added is also studied.

QED loop effects in the spacetime background of a Schwarzschild black hole

The black-hole evaporation implies that the quantum-field propagators in a local Minkowski frame acquire a correction, which gives rise to this process. The modification of the propagators causes, in turn, non-trivial local effects due to the radiative/loop diagrams in non-linear QFTs. In particular, there should be imprints of the evaporation in QED, if one goes beyond the tree-level approximation. Of special interest in this respect is the region near the black-hole horizon, which, already at tree level, appears to show highly non-classical features, e.g., negative energy density and energy flux into the black hole.

The effective Tolman temperature in curved spacetimes

We review a recently proposed effective Tolman temperature and present its applications to various gravitational systems. In the Unruh state for the evaporating black holes, the free-fall energy density is found to be negative divergent at the horizon, which is in contrast to the conventional calculations performed in the Kruskal coordinates. We resolve this conflict by invoking that the Kruskal coordinates could be no longer proper coordinates at the horizon. In the Hartle–Hawking–Israel state, despite the negative finite proper energy density at the horizon, the Tolman temperature is divergent there due to the infinite blueshift of the Hawking temperature. However, a consistent Stefan–Boltzmann law with the Hawking radiation shows that the effective Tolman temperature is eventually finite everywhere and the equivalence principle is surprisingly restored at the horizon. Then, we also show that the firewall necessarily emerges out of the Unruh vacuum, so that the Tolman temperature in the evaporating black hole is naturally divergent due to the infinitely blueshifted negative ingoing flux crossing the horizon, whereas the outgoing Hawking radiation characterized by the effective Tolman temperature indeed originates from the quantum atmosphere, not just at the horizon. So, the firewall and the atmosphere for the Hawking radiation turn out to be compatible, once we discard the fact that the Hawking radiation in the Unruh state originates from the infinitely blueshifted outgoing excitations at the horizon. Finally, as a cosmological application, the initial radiation energy density in warm inflation scenarios has been assumed to be finite when inflation starts. We successfully find the origin of the nonvanishing initial radiation energy density in the warm inflation by using the effective Tolman temperature.

Theoretical investigation on the covalence in AgRnX and XAgRn (X = F - I).

CCSD(T) calculations were performed to investigate the stabilities and interaction mechanisms of the AgRnX and XAgRn (X = F - I) series. Dissociation energies and frontier orbital properties demonstrate an increased trend of stabilities. Ag spd hybrids and Rn/X sp hybrids come into the σAg-Rn and σAg-X bonding orbital. The nature of Ag-Rn, Ag-X and Rn-X interactions were investigated by atoms in molecules (AIM) theory. The negative energy density and positive Laplacian values, as well as small electron densities at bond critical points (BCPs), characterize the moderate strength with partial covalence of interactions. BCP properties (-G/V and G/ρ), electron density deformations and natural resonance theory (NRT) results display increased covalence down the periodic table.

Gedankenexperiment, Assuming Nonsingular Quantum Bounce Friedman Equations Leading to a Causal Discontinuity between Pre Planckian to Planckian Physics Space-Time Regime

This paper is to address using what a fluctuation of a metric tensor leads to, in pre Planckian physics. If so then, we pick the conditions for an equality, with a small δgn, to come up with restraints which are in line with modifications of the Friedman equation in a quantum bounce, with removal of the Penrose theorem initial singularity. In line with super negative pressure being applied, so as to understand what we can present as far as H = 0 (quantum bounce) in terms of density of the Universe. And also considering what to expect when P = wΔρ ~ (-1+e+)Δρ, i.e. we have a negative energy density in Pre Planckian space-time. This leads to a causal discontinuity between Pre Planckian to Planckian space-time due to the sign of the inflaton changing from minus to positive, for reasons brought up in this manuscript, i.e. looking at Equations (9)-(11) of this document, with explanations as to what is going on physically.

Geometrical Properties of Exotic Matter in the Solution of the Einstein–Maxwell Equations of Wormhole Type

On the basis of a new exact solution of the equations of GRT for centrally-symmetric charged dust, the internal structure of a nonstationary time-periodic wormhole with two static necks continued into two asymptoticallyflat vacuum parallel spaces is investigated, and it is shown that the reason for the appearance in some regions of the curved spacetime of a wormhole of negative energy densities of the dustlike matter, which arise when expansion gives way to compression, is a change in the sign of the scalar (Gaussian) curvature of 4-spacetime from positive to negative due to the appearance of two-dimensional coordinate surfaces with principal curvatures of different signs.

Stabilities and interactions of CuRnX and XCuRn (X = F – I): ab initio calculations

ABSTRACTTheoretical investigations on the CuRnX and XCuRn (X = F – I) series have been performed at the CCSD(T) theoretical level. Analyses on dissociation energy and frontier orbital show a decreased trend of stabilities down the periodic table. NBO analyses show the existence of σCu-Rn and σCu-X bonding orbital resulted from the overlap between Cu spd hybrid and Rn/X sp hybrid. The Cu–Rn, Cu–X and Rn–X interactions characterised by negative energy density values, positive Laplacian values and small electron densities at bond critical point (BCP) can be described as interactions of moderate strength with partial covalence. Analyses on electron localisation functions, electron density deformations, BCP properties (−G/V and G/ρ) and natural resonance theory demonstrate an increased covalence down the periodic table.

Some Theorems upon Negative Energy Density of a Quantum Free Scalar Field in an Inertial World Line of the Minkowski Space-Time

Some Theorems upon Negative Energy Density of a Quantum Free Scalar Field in an Inertial World Line of the Minkowski Space-Time

AuRnX and XAuRn (X=F ‐ I and OH)

AbstractSystematic theoretical investigations on the AuRnX and XAuRn (X=F‐I and OH) have been performed at B3LYP, MP2 and CCSD(T) theoretical levels. The linear structures, stretching frequencies and IR intensities were predicted. Analyses on dissociation energies and frontier orbitals show a decreased trend of stability down the periodic table for halogens. Natural bond orbital analyses show the σAu‐Rn and σAu‐X bonding occured between Au spd hybrids and Rn/X sp hybrids. The Au−Rn,Au−X and Rn−X interactions, characterized by negative energy densities and positive Laplacian values together with relative small electron densities at BCPs, can be described as interactions of moderate strength with partial covalence. Analyses on electron localization functions, electron density deformations and bonding orbital coefficients found an increased covalence trend down the periodic table for halogens.

Shadows of Einstein–dilaton–Gauss–Bonnet black holes

We study the shadows of the fully non-linear, asymptotically flat Einstein–dilaton–Gauss–Bonnet (EdGB) black holes (BHs), for both static and rotating solutions. We find that, in all cases, these shadows are smaller than for comparable Kerr BHs, i.e. with the same total mass and angular momentum under similar observation conditions. In order to compare both cases we provide quantitative shadow parameters, observing in particular that the differences in the shadows mean radii are never larger than the percent level. Therefore, generically, EdGB BHs cannot be excluded by (near future) shadow observations alone. On the theoretical side, we find no clear signature of some exotic features of EdGB BHs on the corresponding shadows, such as the regions of negative (Komar, say) energy density outside the horizon. We speculate that this is due to the fact that the Komar energy interior to the light rings (or more precisely, the surfaces of constant radial coordinate that intersect the light rings in the equatorial plane) is always smaller than the ADM mass, and consequently the corresponding shadows are smaller than those of comparable Kerr BHs. The analysis herein provides a clear example that it is the light ring impact parameter, rather than its “size”, that determines a BH shadow.

Spacetime dynamics of a Higgs vacuum instability during inflation

A remarkable prediction of the Standard Model is that, in the absence of corrections lifting the energy density, the Higgs potential becomes negative at large field values. If the Higgs field samples this part of the potential during inflation, the negative energy density may locally destabilize the spacetime. We use numerical simulations of the Einstein equations to study the evolution of inflation-induced Higgs fluctuations as they grow towards the true (negative-energy) minimum. These simulations show that forming a single patch of true vacuum in our past light cone during inflation is incompatible with the existence of our Universe; the boundary of the true vacuum region grows outward in a causally disconnected manner from the crunching interior, which forms a black hole. We also find that these black hole horizons may be arbitrarily elongated---even forming black strings---in violation of the hoop conjecture. By extending the numerical solution of the Fokker-Planck equation to the exponentially suppressed tails of the field distribution at large field values, we derive a rigorous correlation between a future measurement of the tensor-to-scalar ratio and the scale at which the Higgs potential must receive stabilizing corrections in order for the Universe to have survived inflation until today.