Effective Vacuum Energy Research Articles

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.

The effective potential originating from swampland and the non-trivial Brans-Dicke coupling * * Supported by the National Natural Science Foundation of China (11775080, 11865016)

The effective vacuum energy density contributed by the non-trivial contortion distribution and the bare vacuum energy density can be viewed as the energy density of the auxiliary quintessence field potential. We find that the negative bare vacuum energy density from string landscape leads to a monotonically decreasing quintessence potential while the positive one from swampland leads to the metastable or stable de Sitter-like potential. Moreover, the non-trivial Brans-Dicke like coupling between the quintessence field and gravitation field is necessary in the latter case.

Higher-spin gravity and torsion on quantized space-time in matrix models

A geometric formalism is developed which allows to describe the non-linear regime of higher-spin gravity emerging on a cosmological quantum space-time in the IKKT matrix model. The vacuum solutions are Ricci-flat up to an effective vacuum energy- momentum tensor quadratic in the torsion, which arises from a Weitzenböck-type higher spin connection. Torsion is expected to be significant only at cosmic scales and around very massive objects, and could behave like dark matter. A non-linear equation for the torsion tensor is found, which encodes the Yang-Mills equations of the matrix model. The metric and torsion transform covariantly under a higher-spin generalization of volume-preserving diffeomorphisms, which arises from the gauge invariance of the matrix model.

Effective quintessence from string landscape

Recently, Vafa et al. proposed two string swampland criteria, and studying the constraints imposed by the two string swampland criteria on cosmology, they found that the inflationary models are generally difficult to be compatible with these two criteria. Applying these two criteria to the accelerated expansion of the universe during the current period, it was found that the specific quintessence model can satisfy these constraints while satisfying the constraints imposed by the current observations. Applying the gravitational theory of large scale Lorentz violation to cosmology, the vacuum energy density is not the only cause of the accelerated expansion of the universe. The large scale Lorentz violation combined with the cosmological constant term results in the observed accelerated expansion of the late universe. The vacuum energy density is a bit like a naked cosmological constant. The equivalent energy density considering the large scale Lorentz violation effect is the effective cosmological constant that determines the evolution of the universe. In this way, we find that the negative cosmological constant in the string landscape can also accelerate the expansion of the universe, and compared with the <inline-formula><tex-math id="M2">\begin{document}$ {\varLambda _{{\rm{CDM}}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20190282_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20190282_M2.png"/></alternatives></inline-formula> model, it leads to a cosmological constant as an effective vacuum energy density. Effective vacuum energy density behaves as a monotonically decreasing quintessence potential energy for the string landscape, for most of the naked positive vacuum energy densities in the swampland, the evolution of effective cosmological constant with time will show a local minimum. Comparing the calculated results of the distance modulus withthe astronomical observations, we can obtain that a negative cosmological constant also accelerates the expansion of the universe. Thus, the vacuum energy density derived from the string landscape will give quintessence potential that satisfies the swampland criterion, while the evolution of vacuum energy density given by the swampland model of the metastable dS vacuum is not quintessence potential, so it cannot satisfy the second de Sitter criterion. Therefore, the effective potential leading to the accelerated expansion of the late universe can only come from the string landscape, which is naturally UV completion. Therefore, it gives that the accelerated expansion of the late universe is the feature of early quantum gravity. It is not necessary to use the metastable de Sitter vacuum to explain the accelerated expansion of the late universe. The difficulty of incompatibility between the swampland model and the accelerated expansion of the late universe caused by the swampland conjecture will be eliminated.

FROM INFLATION TO DARK ENERGY THROUGH A DYNAMICAL Λ: AN ATTEMPT AT ALLEVIATING FUNDAMENTAL COSMIC PUZZLES

After decades of successful hot big-bang paradigm, cosmology still lacks a framework in which the early inflationary phase of the universe smoothly matches the radiation epoch and evolves to the present "quasi" de Sitter spacetime. No less intriguing is that the current value of the effective vacuum energy density is vastly smaller than the value that triggered inflation. In this paper, we propose a new class of cosmologies capable of overcoming, or highly alleviating, some of these acute cosmic puzzles. Powered by a decaying vacuum energy density, the spacetime emerges from a pure nonsingular de Sitter vacuum stage, "gracefully" exits from inflation to a radiation phase followed by dark matter and vacuum regimes, and, finally, evolves to a late-time de Sitter phase.

Canonical and phantom scalar fields as an interaction of two perfect fluids

In this article we investigate and develop specific aspects of Friedmann-Robertson-Walker (FRW) scalar field cosmologies related to the interpretation that canonical and phantom scalar field sources may be interpreted as cosmological configurations with a mixture of two interacting barotropic perfect fluids: a matter component $\rho_1(t)$ with a stiff equation of state ($p_1=\rho_1$), and an "effective vacuum energy" $\rho_2(t)$ with a cosmological constant equation of state ($p_2=-\rho_2$). An important characteristic of this alternative equivalent formulation in the framework of interacting cosmologies is that it gives, by choosing a suitable form of the interacting term $Q$, an approach for obtaining exact and numerical solutions. The choice of $Q$ merely determines a specific scalar field with its potential, thus allowing to generate closed, open and flat FRW scalar field cosmologies.

Quantum gravity effects in the Kerr spacetime

We analyze the impact of the leading quantum gravity effects on the properties of black holes with nonzero angular momentum by performing a suitable renormalization group improvement of the classical Kerr metric within Quantum Einstein Gravity (QEG). In particular we explore the structure of the horizons, the ergosphere, and the static limit surfaces as well as the phase space avilable for the Penrose process. The positivity properties of the effective vacuum energy momentum tensor are also discussed and the "dressing" of the black hole's mass and angular momentum are investigated by computing the corresponding Komar integrals. The pertinent Smarr formula turns out to retain its classical form. As for their thermodynamical properties, a modified first law of black hole thermodynamics is found to be satisfied by the improved black holes (to second order in the angular momentum); the corresponding Bekenstein-Hawking temperature is not proportional to the surface gravity.

Dynamic vacuum variable and equilibrium approach in cosmology

A modified-gravity theory is considered with a four-form field strength $F$, a variable gravitational coupling parameter $G(F)$, and a standard matter action. This theory provides a concrete realization of the general vacuum variable $q$ as the four-form amplitude $F$ and allows for a study of its dynamics. The theory gives a flat Friedmann-Robertson-Walker universe with rapid oscillations of the effective vacuum energy density (cosmological ``constant''), whose amplitude drops to zero asymptotically. Extrapolating to the present age of the Universe, the order of magnitude of the average vacuum energy density agrees with the observed near-critical vacuum energy density of the present universe. It may even be that this type of oscillating vacuum energy density constitutes a significant part of the so-called cold dark matter in the standard Friedmann-Robertson-Walker framework.

Dynamical vacuum energy via an adjustment mechanism

A new mechanism of adjustment of vacuum energy down to the observed value from an initially huge one is considered. The mechanism is based on a very strong variation of the gravitational coupling constant in the very early universe. The model predicts that the noncompensated remnant of vacuum energy changes very slowly at late stages of the cosmological evolution and is naturally close to the observed one. Asymptotically the effective vacuum energy tends to a negative value, so the cosmological expansion should stop and turn into contraction. There remains the problem of introduction of the usual matter into the model and therefore realizing realistic cosmology.

The anthropic arrow of time and realistic world models: On Price and atemporal universe

In recent attempts at building an atemporal ('tenseless') picture of the physical world, insufficient attention is devoted to processes giving rise to the cosmological arrow of time. Having regard to the new empirical findings and particularly to the epochal discovery of large effective vacuum energy density, the existing discussions of the topic need to be reassessed. In particular, the necessity of a new treatment of asymmetric temporal boundary conditions in an open universe is hereby put forward. Some errors and uncertainties implicit in the recent treatment of the problem of the cosmological arrow of time in the brilliant recent monograph of Prof. Price are briefly discussed. In addition, we discuss relevancy of the high level of complexity observable in living and intelligent beings in the universe for the question of time-reversal symmetry.

On likely values of the cosmological constant

We discuss models in which the smallness of the effective vacuum energy density ${\ensuremath{\rho}}_{\ensuremath{\Lambda}}$ and the coincidence of the time of its dominance ${t}_{\ensuremath{\Lambda}}$ with the epoch of galaxy formation ${t}_{G}$ are due to anthropic selection effects. In such models, the probability distribution for ${\ensuremath{\rho}}_{\ensuremath{\Lambda}}$ is a product of an a priori distribution ${\mathcal{P}}_{*}({\ensuremath{\rho}}_{\ensuremath{\Lambda}})$ and of the number density of galaxies at a given ${\ensuremath{\rho}}_{\ensuremath{\Lambda}}$ (which is proportional to the number of observers who will detect that value of ${\ensuremath{\rho}}_{\ensuremath{\Lambda}}).$ To determine ${\mathcal{P}}_{*},$ we consider inflationary models in which the role of the vacuum energy is played by a slowly varying potential of some scalar field. We show that the resulting distribution depends on the shape of the potential and generally has a non-trivial dependence on ${\ensuremath{\rho}}_{\ensuremath{\Lambda}},$ even in the narrow anthropically allowed range. This is contrary to Weinberg's earlier conjecture that the a priori distribution should be nearly flat in the range of interest. We calculate the (final) probability distributions for ${\ensuremath{\rho}}_{\ensuremath{\Lambda}}$ and for ${t}_{G}{/t}_{\ensuremath{\Lambda}}$ in simple models with power-law potentials. For some of these models, the agreement with the observationally suggested values of ${\ensuremath{\rho}}_{\ensuremath{\Lambda}}$ is better than with a flat a priori distribution. We also discuss a quantum-cosmological approach in which ${\ensuremath{\rho}}_{\ensuremath{\Lambda}}$ takes different values in different disconnected universes and argue that Weinberg's conjecture is not valid in this case as well. Finally, we extend our analysis to models of quintessence, with similar conclusions.

Dilation, winding modes and cosmological solutions

The author reviews some formal aspects of cosmological solutions in closed string theory with duality symmetric 'matter' emphasizing the necessity to account for the dilaton dynamics for a proper incorporation of duality. The author considers two models: when the matter action is the classical action of the fields corresponding to momentum and winding modes and when the matter action is represented by the quantum vacuum energy of the string compactified on a torus. Assuming that the effective vacuum energy is positive one finds that in both cases the scale factor undergoes oscillations from maximal to minimal values with the amplitude of oscillations decreasing to zero or increasing to infinity depending on whether the effective coupling (dilaton field) decreases or increases with time. The contribution of the winding modes to the classical action prevents infinite expansion. Duality is spontaneously broken on a solution with generic initial conditions.

The asymptopia of quasi-local mass and momentum. I. General formalism and stationary spacetimes

The quasi-local measures of mass and momentum introduced by Hawking, Ludvigsen and Vickers and Penrose are calculated for spheres near null infinity. Asymptotic expansion for the connection of an Einstein-Maxwell spacetime are obtained and an expansion of the 2-surface twistor equations is developed. Exact solutions are obtained for stationary spacetimes. For such spacetimes, unphysical contributions to the quasi-local mass found in the Hawking and Ludvigsen-Vickers definitions are eliminated in the twistor construction at the orders considered. In the twistor approach the total angular momentum contributes to the effective vacuum energy density and the absolutely conserved quantities associated with the Maxwell field contribute to the field momentum densities. The angular momentum twistor is found to have the required hermiticity properties with a particular choice of the twistor norm.

Modeling in chaotic relativity

The chaotic behavior of solutions to Einstein's equations has recently been studied by Barrow within the framework of the dynamical systems theory. Barrow's program of gravitational turbulence is implemented in part by considering the solutions of type ${\mathrm{VII}}_{0}$ and IX as well as some intermediate types. Quantitative measures of chaos, such as the power spectrum and Lyapunov characteristic exponent, are computed. By converting the equations of motion for the cosmic scale factors to stochastic Langevin's equations, the Mixmaster cosmology in the presence of driving noise terms is investigated. Possible sources of noise can be attributed to an imperfect cancellation of the effective vacuum energy density and the energy density associated with the Higgs field. An ensemble average over random trajectories leads to the suppression of chaotic behavior for type-IX cosmology.