Search

International audience; We introduce a new logotropic model based on a complex scalar field with a logarithmic potential that unifies dark matter and dark energy. The scalar field satisfies a nonlinear wave equation generalizing the Klein-Gordon equation in the relativistic regime and the Schrödinger equation in the nonrelativistic regime. This model has an intrinsically quantum nature and returns the Λ cold dark matter (CDM) model in the classical limit ℏ→0. It involves a new fundamental constant of physics A/c2=2.10×10-26 g m-3 responsible for the late accelerating expansion of the Universe and superseding the Einstein cosmological constant Λ. The logotropic model is almost indistinguishable from the ΛCDM model at large (cosmological) scales but solves the CDM crisis at small (galactic) scales. It also solves the problems of the fuzzy dark matter model. Indeed, it leads to cored dark matter halos with a universal surface density Σ0th=5.85(A/4πG)1/2=133 M⊙/pc2. This universal surface density is predicted from the logotropic model without adjustable parameter and turns out to be close to the observed value Σ0obs=141-52+83 M⊙/pc2. We also argue that the quantities Ωdm,0 and Ωde,0, which are usually interpreted as the present proportions of dark matter and dark energy in the ΛCDM model, are equal to Ωdm,0th=11+e(1-Ωb,0)=0.2559 and Ωde,0th=e1+e(1-Ωb,0)=0.6955 in very good agreement with the measured values Ωdm,0obs=0.2589 and Ωde,0obs=0.6911 (their empirical ratio 2.669 is close to the Euler number e=2.71828…). We point out, however, important difficulties with the logotropic model, similar to those encountered by the generalized Chaplygin gas model. These problems are related to the difficulty of forming large-scale structures due to an increasing speed of sound as the Universe expands. We discuss potential solutions to these problems, stressing in particular the importance to perform a nonlinear study of structure formation.

In this work, we study tracker phantom dark energy models with a general parameterization of the scalar potentials. Our analysis also considers the scenario of having both phantom field and the cosmological constant as the dark energy components. A detailed statistical analysis with current cosmological observations shows an increase in the value of the Hubble parameter due to the presence of phantom dark energy but it can not alleviate the Hubble tension completely. Our results using Bayesian methods suggests a decisive evidence in favor of a phantom field over a positive cosmological constant, although the possibility of a negative cosmological constant cannot be ruled out hidden in the dark sector.

The Copernican principle (CP), i.e. the assumption that we are not privileged observers of the Universe, is a fundamental tenet of the standard cosmological model. A violation of this postulate implies the possibility that the apparent cosmic acceleration could be explained without the need of a cosmological constant, dark energy or paper we present a new test of the CP relating the distance and the expansion rate, derived via Noether's theorem, which is complementary to other tests found in the literature. We also simulate fiducial data based on upcoming stage IV galaxy surveys and use them to reconstruct the Hubble rate $H(z)$ and the angular diameter distance $d_A(z)$ in order to forecast how well our null test can constrain deviations from the cosmological constant model. We find that our new test can easily rule out several scenarios based on the Lema\^{\i}tre-Tolman-Bondi void model at confidence of $\gtrsim 3\sigma$ at middle to high redshifts ($z>0.5$)., Comment: 8 pages, 1 figure, 2 tables. Changes match published version

We present an improved formulation of 4-dimensional Lorentzian spinfoam quantum gravity with cosmological constant. The construction of spinfoam amplitudes uses the state-integral model of PSL(2,$\mathbb{C}$) Chern-Simons theory and the implementation of simplicity constraint. The formulation has 2 key features: (1) spinfoam amplitudes are all finite, and (2) With suitable boundary data, the semiclassical asymptotics of the vertex amplitude has two oscillatory terms, with phase plus or minus the 4-dimensional Lorentzian Regge action with cosmological constant for the constant curvature 4-simplex., 25 pages, 8 figures

The fractional dark energy (FDE) model describes the accelerated expansion of the Universe through a nonrelativistic gas of particles with a noncanonical kinetic term. This term is proportional to the absolute value of the three-momentum to the power of $3w$, where $w$ is simply the dark energy equation of state parameter, and the corresponding energy leads to an energy density that mimics the cosmological constant. In this paper we expand the fractional dark energy model considering a non-zero chemical potential and we show that it may thermodynamically describe a phantom regime. The Planck constraints on the equation of state parameter put upper limits on the allowed value of the ratio of the chemical potential to the temperature. In the second part, we investigate the system of fractional dark energy particles with negative absolute temperatures (NAT). NAT are possible in quantum systems and in cosmology, if there exists an upper bound on the energy. This maximum energy is one ingredient of the FDE model and indicates a connection between FDE and NAT, if FDE is composed of fermions. In this scenario, the equation of state parameter is equal to minus one and, using cosmological observations, we find that the transition from positive to negative temperatures is allowed at any redshift larger than one., Comment: 11 pages, updated version with constraints from observations, references added

The holographic principle implies that quantum field theory (QFT) overcounts the number of independent degrees of freedom in quantum gravity. An argument due to Cohen, Kaplan, and Nelson (CKN) suggests that the number of degrees of freedom well described by QFT is even smaller than required by holographic bounds, and CKN interpreted this result as indicative of a correlation between the UV and IR cutoffs on QFT. Here, we consider an alternative interpretation in which the QFT degrees of freedom are depleted as a function of scale. We use a simple recipe to estimate the impact of depleted densities of states on precision observables, including the Lamb shift and lepton g−2. Although these observables are not sensitive to the level of depletion motivated by gravitational considerations, the phenomenological exercises also provide an interesting test of quantum field theory that is independent of underlying quantum gravity assumptions. A depleted density of states can also render the QFT vacuum energy UV insensitive, reconciling the success of QFT in describing ordinary particle physics processes and its apparent failure in predicting the cosmological constant.

We find constrained instantons in Einstein gravity with and without a cosmological constant. These configurations are not saddle points of the Einstein-Hilbert action, yet they contribute to non-perturbative processes in quantum gravity. In some cases we expect that they give the dominant contribution from spacetimes with certain fixed topologies. With negative cosmological constant, these metrics describe wormholes connecting two asymptotic regions. We find many examples of such wormhole metrics and for certain symmetric configurations establish their perturbative stability. We expect that the Euclidean versions of these wormholes encode the energy level statistics of AdS black hole microstates. In the de Sitter and flat space settings we find new homogeneous and isotropic bounce and big bang/crunch cosmologies., 6+10 pages, 1 figure; v2: improved discussion of constrained instantons, fixes in proof of perturbative stability

The deflection and gravitational lensing of light and massive particles in arbitrary static, spherically symmetric and asymptotically (anti-)de Sitter spacetimes are considered in this work. We first proved that for spacetimes whose metric satisfying certain conditions, the deflection of null rays with fixed closest distance will not depend on the cosmological constant $\Lambda$, while that of timelike signals and the apparent angle in gravitational lensing still depend on $\Lambda$. A two-step perturbative method is then developed to compute the change of the angular coordinate and total travel time in the weak field limit. The results are quasi-series of two small quantities, with the finite distance effect of the source/detector naturally taken into account. These results are verified by applying to some known de Sitter spacetimes. Using an exact gravitational lensing equation, we solved the apparent angles of the images and time delays between them and studied the effect of $\Lambda$ on them. It is found that generally, a small positive $\Lambda$ will decrease the apparent angle of images from both sides of the lens and increase the time delay between them. The time delay between signals from the same side of the lens but with different energy however, will be decreased by $\Lambda$., Comment: 20 pages, 5 figures

Lambda cold dark matter ( Λ CDM ) is increasingly facing challenges in late-time cosmology, notably in the Hubble parameter H ( z ) at redshift zero known as H 0 -tension. Extensions to Λ CDM have been approached mostly by models with an extra parameter. In this work, we provide a framework for evaluating the viability of models of late-time cosmology by investigating unparticle cosmology as a case study. Unparticle cosmology proposes a scale invariant contribution by a dimensionless parameter δ . We focus on H 0 -tension in comparison with scale invariant and Λ CDM models. The dynamical behavior of unparticle cosmology with and without a cosmological constant shows that for most values of δ ∈ [ − 6 , 1 ] (corresponding to d u ∈ [ − 2 , 3 / 2 ] ), the late-time Universe will be Λ and matter dominated, respectively, with negligible contribution of unparticles. It predicts H ( z ) in the future to be zero or constant, the latter pointing to a stable de Sitter phase for our Universe. Our data analysis shows δ = − 2.06 ± 0.46 as the best fit to the data. Consequently, the conventional value of d u = 3 / 2 ≡ δ = 1 is ruled out by 6.6 σ . However, there is a pronounced gap between the models and what is demanded by observational data in the q Q -diagram for all δ . We conclude that unparticle cosmology fails to come to the rescue of challenges to late-time Λ CDM , but it provides a pointer to holographic dark energy.

In lower dimensions, charged AdS black holes in an extended phase space, where the cosmological constant is interpreted as the thermodynamic pressure, are typically absent of liquid/gas phase transitions. We investigate the criticality of lower dimensional charged, dilatonic, asymptotically AdS (CDAdS$_d$) black holes generated from consistent truncations of RNAdS$_{d+2}$ black objects. We demonstrate that CDAdS$_{d}$ black holes in $d, 10 pages, no figures

Four components of the axisymmetric Einstein equations in 2+1 dimensions with negative cosmological constant can be written as $\nabla_aM=\dots$ and $\nabla_aJ=\dots$, where the dots stand for stress-energy terms, and $M$ and $J$ are scalars. In vacuum, they reduce to the constant mass and angular momentum parameters of the BTZ solution of the same name. The integrability conditions for the Einstein equations give rise to two conserved stress-energy currents $\nabla_aj^a_{(M)}=0$ and $\nabla_aj^a_{(J)}=0$. The angular momentum current is just the Noether current due to axisymmetry, but the mass current is unexpected in the presence of rotation. The conserved quantity $M$ exists in all dimensions in spherical symmetry, known as the Misner-Sharp, Hawking or Kodama mass, but in 2+1 dimensions $M$ exists also in axisymmetry, even with rotation. We use $M$ and $J$ to give a fully constrained formulation of the axisymmetric Einstein equations in 2+1 dimensions, where the Einstein equations are solved by explicit integration from the center along time slices. We use the two conserved matter currents in the construction of a high-resolution shock-capturing formulation of the Einstein-perfect fluid system, in which $M$ and $J$ momentum are then exactly conserved by construction. We demonstrate convergence of the code in the test cases of generic dispersion and collapse and stable and unstable rotating stars., Comment: 23 pages, 17 figures, Typos corrected. This version has been accepted by PRD

We analyze the canonical quantum dynamics of the isotropic universe, as emerging from the Hamiltonian formulation of a metric $f(R)$ gravity, viewed in the Jordan frame. The canonical method of quantization is performed by solving the Hamiltonian constraint before quantizing and adopting like a relational time the nonminimally coupled scalar field emerging in the Jordan frame. The resulting Schr\"odinger evolution is then investigated both in the vacuum and in the presence of a massless scalar field, though as the kinetic component of an inflaton. We show that, in vacuum, the morphology of localized wave packets is that of a nonspreading profile up to the cosmological singularity. When the external scalar field is included into the dynamics, we see that the wave packets acquire the surprising feature of increasing localization of the universe volume, as it expands. This result suggests that, in the metric $f(R)$ formulation of gravity, a spontaneous mechanism arises for the Universe classicalization. Actually, when the phase space of the scalar field is fully explored, such an increasing localization in the Universe volume is valid up to a given value of the time, i.e., of the nonminimally coupled mode after which the wave packets spread again. We conclude our analysis by inferring that before this critical transition age is reached, the inflationary phase could take place, here modeled via a cosmological constant. This point of view provides an interesting scenario for the transition from a Planckian Universe to a classical de-Sitter phase, which in the $f(R)$ gravity appears more natural than in the Einsteinian picture.

In this study, a scalar field propagating in a higher-dimensional Reissner-Nordstr\"om-de Sitter black hole is investigated. Scalar fields are assumed to have non-minimal coupling to the brane or bulk scalar curvature. Five different {definitions} of black hole temperatures are discussed: temperature based on surface gravity, Bousso-Hawking temperature, and three effective temperatures. The greybody factors of minimally and non-minimally coupled scalar fields on the brane and in the bulk are examined under the effect of particle and spacetime properties. The energy emission spectra of black holes are determined at various temperatures for both the brane and bulk channels. The energy emission rates at the Bousso-Hawking temperature are found to be dominant over those at other temperatures. The energy emission curves are suppressed by the presence of coupling parameters. Finally, the bulk-over-brane emission ratios are calculated. Notably, bulk dominance becomes possible for a certain definition of the temperatures and regime of the cosmological constant., Comment: 36 pages, 33 figures, published in PRD

We examine the status of the Chern-Simons (or Kodama) state from the point of view of a formulation of gravity that uses only real connection and metric variables and a real action. We may package the real connection variables into the complex self-dual Ashtekar connection (and will do so to make contact with previous work), but that operation is essentially cosmetic and can be undone at any step or even bypassed altogether. The action will remain the (real) Einstein-Cartan action, forgoing the addition of the usual Holst (or Nieh-Yan) term with an imaginary coefficient. It is then found that the constraints are solved by a modification of the Chern-Simons state which is a pure phase (in the Lorentzian theory, we stress), the phase containing only the fully gauge-invariant imaginary part of the Chern-Simons functional. Thus, the state for the ``real theory'' is nonpathological with regards to the most egregious criticisms facing its ``nonreal'' cousin, solving the complex theory. A straightforward modification of the real Chern-Simons state is also a solution in quasitopological theories based on the Euler invariant, for which the cosmological constant, $\mathrm{\ensuremath{\Lambda}}$, is dynamical. In that case it is enough to shift the usual factor of $\mathrm{\ensuremath{\Lambda}}$ in the wave function to the inside of the spatial Chern-Simons integral. The trick only works for the quasi-Euler theory with a critical coupling previously identified in the literature. It does not apply to the quasi-Pontryagin theory.

The Planck mass and the cosmological constant determine the minimum and the maximum distances in the physical universe. A relativistic theory that takes into account a fundamental distance limit $\ell$ on par with the fundamental speed limit $c$, is based on the de Sitter extension of the Lorentz symmetry. This article proposes a new de Sitter gauge theory of gravity which allows the consistent cosmological evolution of the $\ell$. The theory is locally equivalent to Dirac's scale-invariant version of general relativity, and suggests a novel non-singular extension of cosmology., 9 pages, 0 figures

We consider a theory of $N$ self-interacting quantum scalar fields with quartic $O(N)$-symmetric potential, with a coupling constant $\lambda$, in a generic curved spacetime. We analyze the renormalization process of the Semiclassical Einstein Equations at leading order in the $1/N$ expansion for different renormailzation schemes, namely: the traditional one that sets the geometry of the spacetime to be Minkowski at the renormalization point, and new schemes (originally proposed in [1,2]) which set the geometry to be that of a fixed de Sitter spacetime. In particular, we study the quantum backreaction for fields in de Sitter spacetimes with masses much smaller than the expansion rate $H$. We find that the scheme that uses the classical de Sitter background solution at the renormalization point, stands out as the most appropriate to study the quantum effects on de Sitter spacetimes. Adopting such scheme we obtain the backreaction is suppressed by $H^2/M_{pl}^2$ with no logarithmic enhancement factor of $\ln{\lambda}$, giving only a small screening of the classical cosmological constant due to the backreaction of such quantum fields. We point out the use of the new schemes can also be more appropriate than the traditional one to study quantum effects in other spacetimes relevant for cosmology.

The Schr\"odinger equation with a harmonic potential coupled to the Poisson equation, called the Schr\"odinger-Newton-Hooke (SNH) system, has been considered in a variety of physical contexts, ranging from quantum mechanics to general relativity. Our work is directly motivated by the fact that the SNH system describes the nonrelativistic limit of the Einstein-massive-scalar system with negative cosmological constant. With this paper we begin the investigations aiming at understanding solutions of the SNH system in the energy supercritical spatial dimensions $d\ensuremath{\ge}7$, where we expect to observe interesting short wavelength behaviors due to the confinement of waves by the trapping potential. Here we study spherically symmetric stationary solutions and prove the existence of one-parameter families of nonlinear ground and excited states. The frequency of the ground state as the function of the central density is shown to exhibit different qualitative behaviors in dimensions $7\ensuremath{\le}d\ensuremath{\le}15$ and $d\ensuremath{\ge}16$, which is expected to affect the stability properties of the ground states in these dimensions. Our results bear many similarities to the analogous problem that has been studied for the Gross-Pitaevskii equation.

A new set of field equations for a space-time dependent Newton's constant $G(x)$ and cosmological constant $\Lambda(x)$ in the presence of matter is presented. We prove that it represents the most general mathematically consistent, physically plausible, set of evolution equations assuming at most second derivatives in the dynamical variables. In the new Einstein's equations, only $\Lambda$-kinetic terms arise, while in the modified conservation equation, derivative terms of $G$ also appear. As an application, this formalism is applied in the context of the Asymptotic Safety scenario to the early universe, assuming a perfect fluid with a radiation equation of state. Cosmological solutions are obtained for all types of spatial curvature, displaying a variety of interesting cosmic evolutions. As an indication of such behaviours, bouncing solutions, recollapsing solutions or non-singular expanding solutions with a transient acceleration era are discussed in details., Comment: 21 pages, 12 figures, to appear in PRD

All axisymmetric solutions to the near-horizon geometry equation with a cosmological constant defined on a topological $2$-sphere were derived. The regularity conditions preventing cone singularity at the poles were accounted for. The one-to-one correspondence of the solutions with the extremal horizons in the Kerr-(anti-)de Sitter spacetimes was found. A solution corresponding to the triply degenerate horizon was identified and characterized. The solutions were also identified among the solutions to the Petrov type D equation., 13 pages, no figures, 1 table

A rapid transition of the dark energy equation of state parameter $w$ at a transition redshift $z_t z_t$ to $w z_t$. Such a Late $w$ Phantom Transition ($LwPT$) avoids the discontinuity of $H(z)$ suggested in previous studies and thus does not require a step in the Pantheon Hubble diagram which is strongly constrained. We demonstrate that such an ultra low $z$ abrupt feature of $w(z)$ provides a better fit to cosmological data compared to smooth late time deformations of $H(z)$ that also address the Hubble tension. The strongly present day phantom dark energy behavior implied by this class of models hints towards a rapid approach of a Big Rip singularity which for $z_t=0.02$ will rip the universe in less than 3.5 billion years. Early hints of such effect may be observable in the dynamics of the nearest and largest bound systems ({\it e.g.} Virgo structures). The $LwPT$ can be generically induced by a phantom scalar field frozen by Hubble friction mimicking the cosmological constant and currently entering its ghost instability phase as Hubble friction decreases below the field dynamical scale.

We study static spherically symmetric solutions to the vacuum field equations of quadratic gravity in the presence of a cosmological constant $\Lambda$. Motivated by the trace no-hair theorem, we assume the Ricci scalar to be constant throughout a spacetime. Furthermore, we employ the conformal-to-Kundt metric ansatz that is valid for all static spherically symmetric spacetimes and leads to a considerable simplification of the field equations. We arrive at a set of two ordinary differential equations and study its solutions using the Frobenius-like approach of (infinite) power series expansions. While the indicial equations considerably restrict the set of possible leading powers, careful analysis of higher-order terms is necessary to establish the existence of the corresponding classes of solutions. We thus obtain various non-Einstein generalizations of the Schwarzschild, (anti-)de Sitter [or (A)dS for short], Nariai, and Pleba\'{n}ski-Hacyan spacetimes. Interestingly, some classes of solutions allow for an arbitrary value of $\Lambda$, while other classes admit only discrete values of $\Lambda$. For most of these classes, we give recurrent formulas for all series coefficients. We determine which classes contain the Schwarzschild-(A)dS black hole as a special case and briefly discuss the physical interpretation of the spacetimes. In the discussion of physical properties, we naturally focus on the generalization of the Schwarzschild-(A)dS black hole, namely the Schwarzschild-Bach-(A)dS black hole, which possesses one additional Bach parameter. We also study its basic thermodynamical properties and observable effects on test particles caused by the presence of the Bach tensor. This work is a considerable extension of our letter [Phys. Rev. Lett., 121, 231104, 2018]., Comment: 68 pages, matches the published version + contains the table of contents

We describe an action principle, within the framework of the Eddington gravity, which incorporates the matter fields in a simple manner. Interestingly, the gravitational field equations derived from this action is identical to the Einstein's equations, in contrast with the earlier attempts in the literature. The cosmological constant arises as an integration constant in this approach. In fact, the derivation of the field equations demands the existence of a non-zero cosmological constant, thereby providing the raison d'\^{e}tre for a non-zero cosmological constant, implied by the current observations. Several features of our approach strongly support the paradigm that gravity is an emergent phenomenon and, in this perspective, our action principle could have a possible origin in the microstructure of the spacetime. We also discuss several extensions of the action principle, including the one which can incorporate torsion in the spacetime. We also show that an Eddington-like action can be constructed to obtain the field equations of the Lanczos-Lovelock gravity., Comment: 20 pages, no figures

The classical Eisenhart lift is a method by which the dynamics of a classical system subject to a potential can be recreated by means of a free system evolving in a higher-dimensional curved manifold, known as the lifted manifold. We extend the formulation of the Eisenhart lift to quantum systems, and show that the lifted manifold recreates not only the classical effects of the potential, but also its quantum mechanical effects. In particular, we find that the solutions of the Schrodinger equations of the lifted system reduce to those of the original system after projecting out the new degrees of freedom. In this context, we identify a conserved quantum number, which corresponds to the lifted momentum of the classical system. We further apply the Eisenhart lift to Quantum Field Theory (QFT). We show that a lifted field space manifold is able to recreate both the classical and quantum effects of a scalar field potential. We find that, in the case of QFT, the analogue of the lifted momentum is a quantum charge that is conserved not only in time, but also in space. The different possible values for this charge label an ensemble of Fock spaces that are all disjoint from one another. The relevance of these extended Fock spaces to the cosmological constant and gauge hierarchy problems is considered., Comment: 29 pages; minor corrrections and clarifications; submitted to PRD

We derive a formula for the total canonical energy, and its flux, of weak gravitational waves on a de Sitter background., Comment: essentially identical to the version to appear in PRD

Regularized Einstein-Gauss-Bonnet (EGB) theory of gravity in four dimensions is a new attempt to include nontrivial contributions of Gauss-Bonnet term. In this paper, we make a detailed analysis on possible constraints of the model parameters of the theory from recent cosmological observations, and some theoretical constraints as well. Our results show that the theory with vanishing bare cosmological constant, $\Lambda_0$, is ruled out by the current observational value of $w_{de}$, and the observations of GW170817 and GRB 170817A as well. For nonvanishing bare cosmological constant, instead, our results show that the current observation of the speed of GWs measured by GW170817 and GRB 170817A would place a constraints on $\tilde{\alpha}$, a dimensionless parameter of the theory, as $-7.78\times10^{-16}\le \tilde{\alpha} \leq 3.33\times10^{-15}$., Comment: 11 pages, 3 figures; improvements to presentation, some of the content reordered, and new content added to roughly comment about the scalar perturbations, version to be published in PRD

The Penrose process in the vicinity of an extremal Ban\~ados-Teitelboim-Zanelli(BTZ) black hole is studied. Due to the existence of negative cosmological constant, only massless particles could escape to infinity. Hence we analyse the Penrose process by one massless particle collides with another massive particle near the horizon of BTZ black holes. Calculations of the maximum energy extraction efficiency of this process is carried out for both spinless and spinning particles. Our results show that the spinning particle have a higher energy extraction efficiency than the spinless particle. Moreover, our calculation also indicates that the maximum energy extraction efficiency is independent of the value of the cosmological constant of BTZ black holes., Comment: 16 pages,3 figures

In this work we study the thermodynamics of a ($2+1$)-dimensional static black hole under a nonlinear electric field. In addition to standard approaches, we investigate black hole thermodynamic geometry. We compute Weinhold and Ruppeiner metrics and compare the thermodynamic geometries with the standard description for black hole thermodynamics. We further consider the cosmological constant as an additional extensive thermodynamic variable. For thermodynamic equilibrium in three-dimensional space, we compute heat engine efficiency and show that it may be constructed with this black hole.

It was recently discovered that Killing horizons in the generic Kerr-NUT-(anti) de Sitter spacetimes are projectively singular, i.e. their spaces of the null generators have singular geometry. Only if the cosmological constant takes the special value determined by the Kerr and NUT parameters, and the radius of the horizon, then the corresponding horizon does not suffer that problem. In the current paper, the projectively non-singular horizons are investigated. They are found to be cosmological and non-extremal. Every projectively non-singular horizon can be used to define a global completion of the Kerr-NUT-de Sitter spacetime it is contained in. The resulting spacetime extends from $\mathcal{I}^-$ to $\mathcal{I}^+$, has the topology of $\mathbb{R}\times S_3$ and is smooth except for a possible Kerr-like singularity., 11 pages

In this note, we investigate outcomes of a symplectic formula for the gravitational wave charges in general relativity linearized around the de Sitter spacetime. We derive their explicit form at ${\mathcal{I}}^{+}$ in the Bondi frame, compare with the connected Noether expression, and analyze their gauge dependence, which allows us to fix unambiguously the boundary terms. We also discuss the minimal requirements needed to be imposed on the initial data in order to have finite values of charges. Furthermore, we analyze the transformation laws of the energy upon the action of the de Sitter group and discuss their physical interpretation. Finally, we calculate their flux through a cosmological horizon instead of ${\mathcal{I}}^{+}$. We show that in the limit $\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}0$, one recovers the Trautman-Bondi formula, strengthening a recent proposal that one should choose a null surface as a more natural boundary for the astrophysical systems in the presence of the cosmological constant.

Einstein-Cartan theory is an extension of the standard formulation of General Relativity characterized by a non-vanishing torsion. The latter is sourced by the matter fields via the spin tensor, and its effects are expected to be important at very high spin densities. In this work we analyze in detail the physics of Einstein-Cartan theory with Dirac and Maxwell fields minimally coupled to the spacetime torsion. This breaks the $U(1)$ gauge symmetry, which is suggested by the possibility of a torsion-induced phase transition in the early Universe. The resulting Dirac-like and Maxwell-like equations are non-linear with self-interactions as well as having fermion-boson non-minimal couplings. We discuss several cosmological aspects of this theory, including bounces, acceleration phases and matter-antimatter asymmetry in the torsion era, as well as late-time effects such as the generation of an effective cosmological constant, dark energy, and future bounces within cyclic solutions., Comment: 20 pages, 4 figures

We find the symmetry generators for the Friedman equations emanating from a perfect fluid source, in the presence of a cosmological constant term. The relevant dynamics is seen to be governed by two coupled, first order ordinary differential equations, the continuity and the quadratic constraint equation. Arbitrary functions appear in the components of the symmetry vector, indicating the infinity of the group. When the equation of state is considered as arbitrary but ab initio given, previously known results are recovered and/or generalized. When the pressure is considered among the dynamical variables, solutions for models with different equations of state are mapped to each other; thus enabling the presentation of solutions to models with complicated equations of state starting from simple known cases., 19 pages, no figures, Latex2e source file. Minor changes to match published version

We construct novel solutions to the effective Einstein equation with four dimensional cosmological constant on a 3-brane in Randall-Sundrum II scenario. The charged solution is obtained by assuming the existence of localized Maxwell fields on the 3-brane. Timelike and null circular geodesics in the neutral rotating braneworld spacetime with NUT parameter are discussed, and we find that such geodesics cannot occur on the equatorial plane. On non-equatorial planes, timelike circular geodesics can occur for the negative tidal charge, but we cannot find numerical results to support the existence of non-equatorial null circular geodesics., Comment: 21 pages, 4 figures; v2, refs added

We examine analytical, intrinsically non-Abelian, black holes with SU(2) Yang-Mills matter content. Working in the extended thermodynamics scenario of Lovelock black holes we study the phase structure of a four and a five-dimensional spherically symmetric configuration. We work in Gauss-Bonnet-Einstein-Yang-Mills gravity with negative cosmological constant and use Euclidean methods to explore the thermodynamics of the systems. We observe that the solutions belong to the expected universality class of van der Waals and find a reentrant phase transition., Comment: 8 figures

In this paper, we study a class of higher derivative, non-local gravity which admits homogeneous and isotropic non-singular, bouncing universes in the absence of matter. At the linearized level, the theory propagates only a scalar degree of freedom, and no vector or tensor modes. The scalar can be made free from perturbative ghost instabilities, and has oscillatory and bounded evolution across the bounce., Comment: 5 pages, 1 figure

In this paper, we explore the formation of the marginally trapped/ antitrapped surfaces that arise from the evolution of dust in $D$-dimensions with and without the cosmological constant. We obtain analytical expressions for such surfaces. We also derive closed form expressions for the norms of various quantities that decide the Causal nature of the marginally trapped/antitrapped surfaces. We discuss several interesting features of evolution of these surfaces that are significantly different from the four dimensional counterpart. We obtain the expressions for the Ashtekar-Badrikrihnan's area-balance law for dynamical horizon (spacelike surface) tailored for the case of spherically symmetric dust evolution in $D$-dimensions.

We investigate the cosmological applications of Myrzakulov $F(R,T)$ gravity. In this theory ones uses a specific but nonspecial connection, and thus both curvature and torsion are dynamical fields related to gravity. We introduce a parametrization that quantifies the deviation of curvature and torsion scalars form their corresponding values obtained using the special Levi-Civita and Weitzenb\"ock connections, and we extract the cosmological field equations following the minisuperspace procedure. Even for the simple case where the action of the theory is linear in $R$ and $T$, we find that the Friedmann equations contain new terms of geometrical origin, reflecting the nonspecial connection. Applying the theory at late times we find that we can acquire the thermal history of the universe, where dark energy can be quintessencelike or phantomlike, or behave exactly as a cosmological constant and thus reproducing $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology. Furthermore, we show that these features are obtained for other Lagrangian choices, too. Finally, early-time application leads to the de Sitter solution, as well as to an inflationary realization with the desired scale-factor evolution.

In this study, we consider three dark energy models in which $\mathrm{\ensuremath{\Lambda}}$ is not constant, but has a dynamic nature that depends on the Hubble parameter $H$ and/or its time derivative $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{H}$. We analyze the generalized running vacuum model, for which $\mathrm{\ensuremath{\Lambda}}(H)=A+B{H}^{2}+C\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{H}$, along with the two models obtained by setting $B$ or $C$ equal to zero. A null value for $C$ yields the classical running vacuum model (RVM), while $B=0$ corresponds to what we term the generalized running vacuum subcase, or GRVS. Our main aim is to investigate whether these models can accommodate nonzero spatial curvature. To this end, we carry out a Markov chain Monte Carlo analysis using data for the observables associated with type-Ia supernovae, cosmic chronometers, the cosmic microwave background, and baryon acoustic oscillations, as well as two values for the Hubble constant. Then we include data relating to the growth of large-scale structure (LSS) and repeat the procedure. Our results indicate that taking LSS observations into account helps to tighten constraints and determine a definite sign for the model parameters. In the case of the RVM and GRVS, the addition of growth data result in dynamical vacuum energy being preferred to a cosmological constant at a little over $1\ensuremath{\sigma}$. This happens in both the flat and nonflat scenarios---there are only a few exceptions---but comes at the cost of an extra parameter, which can degrade the performance of the models (as assessed by model selection criteria). Of special relevance is the fact that the inclusion of LSS data appear to increase compatibility with a flat geometry. It also brings the constraints on the Hubble constant closer to the range of values established by Planck.

Based on tensions between the early and late time cosmology, we proposed a double valued cosmological constant which could undergo a phase transition in its history. It is named ``double-$\mathrm{\ensuremath{\Lambda}}$ Cold Dark Matter'': $\mathrm{\ensuremath{\Lambda}}\phantom{\rule[-0.0ex]{-0.45em}{0.0ex}}\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. The phase transition occurred because of (micro-) structures for the dark sector with a proper (local) interaction. In this paper, inspired by the physics of critical phenomena, we study a simplified model such that the cosmological constant has two values before a transition scale factor, ${a}_{t}$, and afterwards it becomes single valued. We consider both the background and perturbation datasets including cosmic microwave background (CMB), Baryon acoustic oscillations (BAO) distances, and R19 data points. $\mathrm{\ensuremath{\Lambda}}\phantom{\rule[-0.0ex]{-0.45em}{0.0ex}}\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ has its maximum likelihood for ${a}_{t}=0.85{1}_{+0.027}^{+0.12}$ and gives ${H}_{0}={72.2}_{\ensuremath{-}1.5}^{+2.2}$. This result shows no inconsistency between early and late time measurements of the Hubble parameter in the $\mathrm{\ensuremath{\Lambda}}\phantom{\rule[-0.0ex]{-0.45em}{0.0ex}}\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. In comparison to $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, our model has better fit to data with $\mathrm{\ensuremath{\Delta}}{\ensuremath{\chi}}^{2}=\ensuremath{-}16$ and we even have a better Akaike information criterion (AIC) quantity $\mathrm{\ensuremath{\Delta}}\mathrm{AI}\mathrm{C}=\ensuremath{-}12$, where our model is penalized because of two more degrees of freedom. We conclude that a phase transition in the behavior of dark energy can address ${H}_{0}$ tension successfully and may be responsible for the other cosmological tensions.

We study the New Massive Gravity extended by the curvature cubed invariant and the Cosmological Constant using the tree-level scattering amplitudes on a maximally symmetric space-time. We identify the parameter space, consisting of the ratio between C.C. and graviton mass squared and the relative coupling strength between curvature squared and cubed invariants, for which the massive spin-2 is a ghost. Different phases of this model are also discussed., 1+10 pages, 3 figures; v2: comments added; published in PRD

We show that a spin-5/2 field can be consistently coupled to gravitation without cosmological constant in five-dimensional spacetimes. The fermionic gauge "hypersymmetry" requires the presence of a finite number of additional fields, including a couple of U(1) fields, a spinorial two-form, the dual of the graviton (of mixed (2,1) Young symmetry) and a spin-3 field. The gravitational sector of the action is described by the purely quadratic Gauss-Bonnet term, so that the field equations for the metric are of second order. The local gauge symmetries of the full action principle close, without the need of auxiliary fields, for a suitable extension of the "hyper-Poincaré" algebra. Apart from the Poincaré and spin-3/2 generators, it includes a generator of spin 2 and a U(1) central extension. Noteworthy, the algebra admits an invariant trilinear form, and its generators allow us to precisely accommodate the entire field content within a single connection, so that the hypergravity action can be formulated as a gauge theory described by a Chern-Simons form in five dimensions., SCOPUS: ar.j, info:eu-repo/semantics/published

The discovery of new four-dimensional black hole solutions presents a new approach to understand the Gauss-Bonnet gravity in low dimensions. In this paper, we test the Gauss-Bonnet gravity by studying the phase transition and microstructures for the four-dimensional charged AdS black hole. In the extended phase space, where the cosmological constant and the Gauss-Bonnet coupling parameter are treated as thermodynamic variables, we find that the thermodynamic first law and the corresponding Smarr formula are satisfied. Both in the canonical ensemble and grand canonical ensemble, we observe the small-large black hole phase transition, which is similar to the case of the van der Walls fluid. This phase transition can also appear in the neutral black hole system. Furthermore, we construct the Ruppeiner geometry, and find that besides the attractive interaction, the repulsive interaction can also dominate among the microstructures for the small black hole with high temperature in a charged or neutral black hole system. This is quite different from the five-dimensional neutral black hole, for which only dominant attractive interaction can be found. The critical behaviors of the normalized scalar curvature are also examined. These results will shed new light into the characteristic property of four-dimensional Gauss-Bonnet gravity., 17 pages, 9 figures, and 2 tables, references added. Accepted for publication in PRD

A new component added to the standard model of cosmology that behaves like a cosmological constant at early times and then dilutes away as radiation or faster can resolve the Hubble tension. We show that a rolling axion coupled to a non-Abelian gauge group exhibits the behavior of such an extra component at the background level and can present a natural particle-physics model solution to the Hubble tension. We compare the contribution of this bottom-up model to the phenomenological fluid approximation and determine that CMB observables sensitive only to the background evolution of the Universe are expected to be similar in both cases, strengthening the case for this model to provide a viable solution to the Hubble tension., Comment: 5 pages, 2 figures. v2: We added clarifications, additional references, and condensed the paper to fit journal guidelines. v2 matches the published version

We perform a study both statistical and theoretical for cosmological models of matter creation and their ability to describe effective phantom models of dark energy. Such models are beyond the ΛCDM model since the resulting cosmic expansion is not adiabatic. In fact, we show that this approach exhibits transient phantom/quintessence scenarios at present time and tends to the standard cosmological model at some stage of the cosmic evolution. We discuss some generalities of the thermodynamics properties for this type of cosmological model; we emphasize on the behavior of the temperature associated to dark matter, which keeps positive along cosmic evolution together with the entropy. The enrichment of this type of model by means of the incorporation of cosmological constant and dissipative effects in the fluid description to explore their cosmological consequences in the expansion of the Universe is considered. Finally, a generalization for the matter production rate as an inhomogeneous expression of the Hubble parameter and its derivatives is discussed; as in all the cases examined, such election leads to an effective phantom/quintessence behavior., This work has been supported by S. N. I. (CONACyTMexico) (M. C.) and by MINECO (Spain), FIS2016-76363-P, and by Project No. 2017 SGR247 (AGAUR, Catalonia) (S. D. O). This work is also supported by MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas “Cosmic Acceleration” No. 15H05890 (S. N.) and the JSPS Grant-in-Aid for Scientific Research (C) No. 18K03615 (S. N.).

A $(3+1)$-dimensional Einstein-Gauss-Bonnet theory of gravity has been recently formulated in [D. Glavan and C. Lin, Phys. Rev. Lett. {\bf 124}, 081301 (2020)] which is different from the pure Einstein theory, i.e., bypasses the Lovelock's theorem and avoids Ostrogradsky instability. The theory was formulated in $D > 4$ dimensions and its action consists of the Einstein-Hilbert term with a cosmological constant, while the Gauss-Bonnet term multiplied by a factor $1/(D-4)$. Then, the four-dimensional theory is defined as the limit $D \to 4$. Here we generalize this approach to the four-dimensional Einstein-Lovelock theory and formulate the most general static $4D$ black-hole solution allowing for a $\Lambda$-term (either positive or negative) and the electric charge $Q$. As metric functions cannot be found in a closed form in the general case, we develop and share publicly the code which constructs the metric functions for every given set of parameters., Comment: 5 pages, 1 ancillary Mathematica(R) notebook

Difference in pressure during expansion and contraction stages of the cosmic evolution can result in a hysteresislike phenomenon in nonsingular cyclic models sourced with a massive scalar field. We discuss this phenomenon for spatially closed isotropic spacetimes in loop quantum cosmology (LQC) for a quadratic and a coshlike potential, with and without a negative cosmological constant using an effective spacetime description of the underlying quantum geometry. Two inequivalent loop quantizations are investigated---one based on holonomies of the Ashtekar-Barbero connection using closed loops, and another based on the connection operator. Due to the underlying quantum geometric effects, both of the models avoid classical singularities, but unlike the holonomy based quantization, the connection based quantization results in two quantum bounces. In spite of the differences in nonsingular effective dynamics of both of the models, the phenomena of hysteresis is found to be robust for the ${\ensuremath{\phi}}^{2}$ potential. Quasiperiodic beats exist for the coshlike potential, irrespective of the nature of the classical recollapse whether by the spatial curvature, or a negative cosmological constant. An interplay of the negative cosmological constant and the spatial curvature in the presence of potentials results in rich features such as islands of cluster of bounces separated by an accelerated expansion and a universe which either undergoes a steplike expansion with multiple turnarounds or quasiperiodic beats depending on a ``tuning'' of the steepness parameter of the potential.

We study the cosmological constant ($\Lambda$) in the standard $\Lambda$CDM model by introducing the \textit{graduated dark energy} (gDE) characterised by a minimal dynamical deviation from the null inertial mass density of the $\Lambda$ in the form $\rho_{\rm inert}\propto \rho^{\lambda}, Comment: 14 pages, 7 figures, 2 tables; matches the version to appear in PRD

Using an alternative approach, we investigate critical behavior and phase transition of higher dimensional charged black holes in an anti--de Sitter background and in the presence of conformally invariant Power-Maxwell electrodynamics. In this approach, we keep the cosmological constant (pressure) as a fixed thermodynamic quantity and instead allow the charge of the black hole to vary. We disclose that one can realize the critical behavior for the system in ${\mathbit{Q}}_{p}\text{\ensuremath{-}}\mathrm{\ensuremath{\Psi}}$ plane and deduce all the critical exponents of the system as well as calculate the critical point $({T}_{c},{\mathbit{Q}}_{{p}_{c}},{\mathrm{\ensuremath{\Psi}}}_{c})$, where ${\mathbit{Q}}_{p}={Q}^{2p/(2p\ensuremath{-}1)}$, $p$ is the power parameter of the Power-Maxwell Lagrangian, and $\mathrm{\ensuremath{\Psi}}$ is the conjugate of ${\mathbit{Q}}_{p}$. We observe that the critical exponents are independent of the details of the model and have the same values as Van der Waals liquid-gas system. We thus complete the analogy of these types of black holes with Van der Waals liquid-gas system. We also write down the equation of state as ${\mathbit{Q}}_{p}={\mathbit{Q}}_{p}(T,\mathrm{\ensuremath{\Psi}})$ and construct a Smarr relation based on this new phase space as $M=M(S,P,{\mathbit{Q}}_{p})$. We obtain the Gibbs free energy of the system and find a swallowtail behavior in Gibbs diagrams, which is a characteristic of the first-order phase transition. Finally, we explain the microscopic behavior of the black hole by using thermodynamic geometry. We observe a gap in the scalar curvature $R$ that occurs between small and large black holes. The maximum value of this gap increases with increasing the dimension of the spacetime. It is seen that the interaction among the internal constituents of the black hole, as a thermodynamical system, is intrinsically a strong repulsive interaction.

We obtain two exact solutions of Einstein gravity coupled to nonlinear electrodynamics (NLED) in $(2+ 1)$-dimensional Anti-de Sitter (AdS) spacetime. The solutions are characterized by the mass $M$, angular momentum $J$, cosmological constant or (anti) de Sitter parameter $\Lambda$, and an electromagnetic parameter $Q$, that is related to an electric field in the first solution and to a magnetic charge for the second solution. Depending on the range of the parameters, the solutions admit a charged rotating asymptotically AdS black hole (BH) interpretation or a charged rotating asymptotically AdS traversable wormhole (WH). If the electromagnetic field is turned off, the stationary Ba\~nados-Teitelboim-Zanelli (BTZ) BH is recovered; in such a way that our BH-WH solutions are nonlinear charged generalizations of the stationary BTZ-BH. Moreover, in contrast to the BTZ metric, the derived AdS solutions are singular at certain radius $r_{s} \neq 0$, resembling the ring singularity of the Kerr-Newman spacetime; while if $\Lambda$ is positive the curvature invariants of the second solution are finite., Comment: 24 pages, 8 figures

A matter-coupled scalar field model is presented to obtain a scalar fifth force when the constraint of the current cosmological constant is satisfied. The interaction potential energy density between the scalar field and matter has a symmetry-breaking form with two potential wells. We prove that the cosmological constant is a value of the scalar field's self-interaction potential energy density at the minimum of the effective matter-density-dependent potential energy density. The effective potential is a sum of the interaction potential and the self-interaction potential of the scalar field. The scalar field can stably sit at the minimum; then the time-dependent cosmological ``constant'' behaves like a constant. The scheme does not conflict with chameleon no-go theorems. However, since the quintessence is trapped by one of the interaction potential wells, the observed cosmic acceleration can be accounted for by the scalar field. The scalar field is also extrapolated to account for inflation at the inflationary era of the Universe. In this era matter fluid is relativistic, and the interaction potential wells vanish. The unconfined quintessence therefore dominates the evolution of the Universe. We conclude that Planck 2018 results favor the closed space of the Universe. The reasons for this are the measured value of the current Hubble constant and the observation of a concave potential in the framework of single-field inflationary models. By invoking a pseudopotential in the inflationary era, the concave feature can be attributed to the pseudopotential, although the self-interaction potential is a convex function. The pseudopotential is defined by a sum of the self-interaction potential and the energy density scale of the curvature of the Universe. The positive curvature leads to the concave feature of the pseudopotential. Within the constraints of the cosmological constants, including the maximum cosmological constant in the inflationary era, we find that the strength of the fifth force is large compared with gravity. Due to the short range of the interaction, the local test of gravity is satisfied. The coupling coefficient denoting the force strength is inversely proportional to the ambient density, while the interaction range is inversely proportional to the square root of the density. For the current matter density $\ensuremath{\sim}{10}^{\ensuremath{-}27}\text{ }\text{ }\mathrm{kg}/{\mathrm{m}}^{3}$ of the Universe, the corresponding interaction range is $\ensuremath{\sim}5\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ and the coupling coefficient is $\ensuremath{\sim}1{0}^{31}$. Since the fifth force is localized in an extreme thin shell, experiments might be designed so that the test objects can pass through the thin shell.

We consider the possibility that, in the semiclassical Einstein equation for cosmological spacetimes, gravity is sourced by the amount of stress-energy that is above that of the instantaneous ground state. For this possibility to be consistent, the Bianchi identities must continue to hold. This is nontrivial because it means that the ground state expectation value of the stress-energy tensor must be covariantly conserved in spite of the fact that the ground state is generally a different state at different times. We prove that this consistency condition does hold. As a consequence, we find that the vacuum stress-energy which is above the instantaneous ground state does not renormalize the cosmological constant, as long as the instantaneous ground states and the instantaneous adiabatic vacua exist., Comment: 15 pages, 1 figure. Accepted to PRD