Non-vanishing Cosmological Constant Research Articles

W_{1+∞} Algebra with a Cosmological Constant and the Celestial Sphere.

It is shown that there exists a simple deformed version of Strominger's infinite-dimensional w_{1+∞} algebra of soft graviton symmetries, which we conjecture to arise in spacetimes with a nonvanishing cosmological constant. The deformed algebra contains a subalgebra generating SO(1,4) or SO(2,3) symmetry groups of dS_{4} or AdS_{4}, depending on the sign of the cosmological constant. The transformation properties of soft gauge symmetry currents under the deformed w_{1+∞} are also discussed.

On curvature related geometric properties of Hayward black hole spacetime

This paper is devoted to the study of curvature properties of Hayward black hole (briefly, HBH) spacetime, which is a solution of Einstein field equations (briefly, EFE) having non-vanishing cosmological constant. We have proved that the HBH spacetime is an Einstein manifold of level 2, 2-quasi Einstein, generalized quasi-Einstein and Roter type manifold. Also, it is shown that the nature of the HBH spacetime is pseudosymmetric and it obeys several types of pseudosymmetries, such as, pseudosymmetry due to concircular, conformal and conharmonic curvature (i.e., F⋅F=LQ(g,F) for F=W,C,K with a smooth scalar function L), and it also possesses the relation R⋅R−LQ(g,C)=Q(S,R). It is engrossing to mention that the nature of energy momentum tensor of the HBH spacetime is pseudosymmetric. On the basis of curvature related properties, we have made a comparison among Reissner–Nordström spacetime, interior black hole spacetime and HBH spacetime. It is noteworthy to mention that the gravitational force of the point-like global monopole spacetime is much stronger than that of HBH spacetime. Also, it is shown that the HBH spacetime admits an almost η-Ricci soliton as well as an almost η-Ricci-Yamabe soliton. Finally, an elegant comparative study is delineated between the HBH spacetime and the point-like global monopole spacetime with respect to different kinds of symmetry, such as, motion, curvature collineation, curvature inheritance etc.

Stars and junction conditions in Einstein–Gauss–Bonnet gravity

The junction conditions for a higher dimensional spherically symmetric charged and anisotropic static star are derived in Einstein–Gauss–Bonnet (EGB) gravity with nonvanishing cosmological constant. It is shown that for a timelike boundary hypersurface of zero thickness, the generalised matching conditions across this surface in EGB gravity are satisfied. A sufficient condition is that the Israel-Darmois conditions are valid. Therefore it is possible to generate a complete stellar model in EGB gravity. The interior matches to the exterior higher dimensional charged Boulware–Deser spacetime with cosmological constant. The barotropic radial pressure has to vanish at the boundary of the star which is also the case in general relativity.

The power spectrum of cosmological number densities

This paper studies the cosmological power spectrum (PS) of the differential and integral galaxy volume number densities, respectively, \(\gamma _i\) and \(\gamma _i^{*}\), constructed with the cosmological distances \(d_i\) \((i={\scriptstyle A},{\scriptstyle G},{\scriptstyle L},{\scriptstyle Z})\), where \(d_{\scriptscriptstyle A}\) is the angular diameter distance, \(d_{\scriptscriptstyle G}\) is the galaxy area distance, \(d_{\scriptscriptstyle L}\) is the luminosity distance and \(d_z\) is the redshift distance. Theoretical and observational quantities were obtained in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime with a non-vanishing cosmological constant. The radial correlation \(\Xi _i\), a quantity defined in the context of these densities, is also discussed in the wave number domain. All observational quantities were computed using luminosity function (LF) data obtained from the FORS Deep Field (FDF) galaxy survey. The theoretical and observational power spectra of \(\gamma _i\), \(\gamma _i^{*}\), \(\Xi _i\) and the ratio \(\gamma _i / \gamma _i^*\) were calculated by performing Fourier transforms on values of these densities which were previously derived by Iribarrem (Astron. Astrophys. 539:A112, 2012) from the observational values \([\gamma ]_{{\textstyle {\scriptscriptstyle \mathrm {obs}}}}\) and \([\gamma ^*]_{{\textstyle {\scriptscriptstyle \mathrm {obs}}}}\) obtained by using the galactic absolute magnitudes and Schechter’s parameters of the galaxy LF presented in Gabasch (Astron. Astrophys. 421:41–58, 2004; Astron. Astrophys. 448:101, 2006). These parameters were evaluated from a I-band selected dataset of the FDF in the redshift range \(0.5 \le z \le 5.0\) for its blue bands and \(0.75 \le z \le 3.0\) for its red ones. The results show similar behavior of the power spectra obtained from \(\gamma \) and \(\gamma ^{*}\) using \(d_{\scriptscriptstyle L}\), \(d_z\) and \(d_{\scriptscriptstyle G}\) as distance measures. The PS of the densities defined with \(d_{\scriptscriptstyle A}\) have a different and inconclusive behavior because this cosmological distance reaches a maximum at \(z\approx 1.6\) in the adopted cosmological model. For the other distances, our results suggest that the PS of \([\gamma _i]_{{\textstyle {\scriptscriptstyle \mathrm {obs}}}}\), \([\gamma ^*_i]_{{\textstyle {\scriptscriptstyle \mathrm {obs}}}}\) and \([\gamma _i / \gamma ^{*}_i]_{{\textstyle {\scriptscriptstyle \mathrm {obs}}}}\) has a general behavior approximately similar to the power spectra obtained with the galaxy two-point correlation function and, by being sample size independent, they may be considered as alternative analytical tools to study the galaxy distribution.

ISCOs and OSCOs in the Presence of a Positive Cosmological Constant in Massive Gravity

We study the impact of a non-vanishing (positive) cosmological constant on the innermost and outermost stable circular orbits (ISCOs and OSCOs, respectively) within massive gravity in four dimensions. The gravitational field generated by a point-like object within this theory is known, generalizing the usual Schwarzschild–de Sitter geometry of General Relativity. In the non-relativistic limit, the gravitational potential differs by the one corresponding to the Schwarzschild–de Sitter geometry by a term that is linear in the radial coordinate with some prefactor γ, which is the only free parameter. Starting from the geodesic equations for massive test particles and the corresponding effective potential, we obtain a polynomial of fifth order that allows us to compute the innermost and outermost stable circular orbits. Next, we numerically compute the real and positive roots of the polynomial for several different structures (from the hydrogen atom to stars and globular clusters to galaxies and galaxy clusters) considering three distinct values of the parameter γ, determined using physical considerations, such as galaxy rotation curves and orbital precession. Similarly to the Kottler spacetime, both ISCOs and OSCOs appear. Their astrophysical relevance as well as the comparison with the Kottler spacetime are briefly discussed.

The Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity.

An excruciating issue that arises in mathematical, theoretical and astro-physics concerns the possibility of regularizing classical singular black hole solutions of general relativity by means of quantum theory. The problem is posed here in the context of a manifestly covariant approach to quantum gravity. Provided a non-vanishing quantum cosmological constant is present, here it is proved how a regular background space-time metric tensor can be obtained starting from a singular one. This is obtained by constructing suitable scale-transformed and conformal solutions for the metric tensor in which the conformal scale form factor is determined uniquely by the quantum Hamilton equations underlying the quantum gravitational field dynamics.

Theoretical and observational constraints on regularized 4D Einstein-Gauss-Bonnet gravity

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 $-7.78\times10^{-16}\le \tilde{\alpha} \leq 3.33\times10^{-15}$.

Axial Symmetry Cosmological Constant Vacuum Solution of Field Equations with a Curvature Singularity, Closed Time-Like Curves, and Deviation of Geodesics

In this paper, we present a type D, nonvanishing cosmological constant, vacuum solution of Einstein’s field equations, extension of an axially symmetric, asymptotically flat vacuum metric with a curvature singularity. The space-time admits closed time-like curves (CTCs) that appear after a certain instant of time from an initial space-like hypersurface, indicating it represents a time-machine space-time. We wish to discuss the physical properties and show that this solution can be interpreted as gravitational waves of Coulomb-type propagate on anti-de Sitter space backgrounds. Our treatment focuses on the analysis of the equation of geodesic deviations.

Dark Energy and Cosmological Model

Today the space of our universe is filled with invisible stuff matter which expanding under the action of gravity which was dark matter. In 1990’s astronomical observation and theoretical calculation was leading astrophysicists to believe that not only the dark matter but also there is vacuum empty space filled in universe that is dark energy. It is suggested that the apparently disparate cosmological phenomenon attributed to so called “dark matter” and dark energy arise from quantum level of space -time itself. This creation of space time results in metric expansion. A recent modification of Einstein’s theory of general relativity by Chadwick, Hodgkinson and McDonald incorporate space time expansion. Recent evidence predicts that apparent amount of dark matter increases with age of universe. In addition proposal leads to the same result for the small but non-vanishing cosmological constant, related to dark energy.

Anisotropic 2+1 dimensional black holes by gravitational decoupling

In the present paper, we analyze the well-known 2+1 dimensional black holes (assuming a non-vanishing cosmological constant) in light of the gravitational decoupling by the minimal geometric deformation approach. To illustrate our results, we consider the BTZ geometry as the seed solution to generate new anisotropic ones. To complement the study, the curvature scalars and the energy conditions are analyzed.

Q-deformed 3D loop gravity on the torus

The q-deformed loop gravity framework was introduced as a canonical formalism for the Turaev–Viro model (with ), allowing to quantize 3D Euclidean gravity with a (negative) cosmological constant using a quantum deformation of the gauge group. We describe its application to the 2-torus, explicitly writing the q-deformed gauge symmetries and deriving the reduced physical phase space of Dirac observables, which leads back to the Goldman brackets for the moduli space of flat connections. Furthermore it turns out that the q-deformed loop gravity can be derived through a gauge fixing from the Fock–Rosly bracket, which provides an explicit link between loop quantum gravity (for q real) and the combinatorial quantization of 3D gravity as a Chern–Simons theory with non-vanishing cosmological constant . A side-product is the reformulation of the loop quantum gravity phase space for vanishing cosmological constant , based on holonomies and fluxes, in terms of Poincaré holonomies. Although we focus on the case of the torus as an example, our results outline the general equivalence between 3D q-deformed loop quantum gravity and the combinatorial quantization of Chern–Simons theory for arbitrary graph and topology.

Two-dimensional dilaton gravity theory and lattice Schwarzian theory

We report a holographic study of a two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the cases of nonvanishing and vanishing cosmological constants. Our result shows that the boundary theory of the two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the case of nonvanishing cosmological constants is the Schwarzian term coupled to a dilaton field, while for the case of vanishing cosmological constant, a theory does not have a kinetic term. We also include the higher derivative term [Formula: see text], where [Formula: see text] is the scalar curvature that is coupled to a dilaton field. We find that the form of the boundary theory is not modified perturbatively. Finally, we show that a lattice holographic picture is realized up to the second-order perturbation of boundary cutoff [Formula: see text] under a constant boundary dilaton field and the nonvanishing cosmological constant by identifying the lattice spacing [Formula: see text] of a lattice Schwarzian theory with the boundary cutoff [Formula: see text] of the two-dimensional dilaton gravity theory.

The κ-(A)dS noncommutative spacetime

The (3+1)-dimensional κ-(A)dS noncommutative spacetime is explicitly constructed by quantizing its semiclassical counterpart, which is the κ-(A)dS Poisson homogeneous space. This turns out to be the only possible generalization of the well-known κ-Minkowski spacetime to the case of non-vanishing cosmological constant, under the condition that the time translation generator of the corresponding quantum (A)dS algebra is primitive. Moreover, the κ-(A)dS noncommutative spacetime is shown to have a quadratic subalgebra of local spatial coordinates whose first-order brackets in terms of the cosmological constant parameter define a quantum sphere, while the commutators between time and space coordinates preserve the same structure of the κ-Minkowski spacetime. When expressed in ambient coordinates, the quantum κ-(A)dS spacetime is shown to be defined as a noncommutative pseudosphere.

Bonnor-Melvin universe with a cosmological constant

We generalize the well-known Bonnor-Melvin solution of the Einstein-Maxwell equations to the case of a non-vanishing cosmological constant. The spacetime is again cylindrically symmetric and static but, unlike the original solution, it truly represents a homogeneous magnetic field.

A small non-vanishing cosmological constant from the Krein–Gupta–Bleuler vacuum

We point out a potential relevance between the Krein–Gupta–Bleuler (KGB) vacuum leading to a fully covariant quantum field theory for gravity in de Sitter (dS) spacetime and the observable smallness of the cosmological constant. This may provide a formulation of linear quantum gravity in a framework amenable to developing a more complete theory determining the value of the cosmological constant.

Are Dark Energy and Dark Matter Different Aspects of the Same Physical Process?

It is suggested that the apparently disparate cosmological phenomena attributed to so-called ‘dark matter’ and ‘dark energy’ arise from the same fundamental physical process: the emergence, from the quantum level, of spacetime itself. This creation of spacetime results in metric expansion around mass points in addition to the usual curvature due to stress-energy sources of the gravitational field. A recent modification of Einstein’s theory of general relativity by Chadwick, Hodgkinson, and McDonald incorporating spacetime expansion around mass points, which accounts well for the observed galactic rotation curves, is adduced in support of the proposal. Recent observational evidence corroborates a prediction of the model that the apparent amount of ‘dark matter’ increases with the age of the universe. In addition, the proposal leads to the same result for the small but nonvanishing cosmological constant, related to ‘dark energy,’ as that of the causet model of Sorkin et al.

Polynomial BF -type action for general relativity and anti-self-dual gravity

We report a gravitational $BF$-type action principle propagating two (complex) degrees of freedom that, besides the gauge connection and the $B$ field, only employs an additional Lagrange multiplier. The action depends on two parameters and remarkably is polynomial in the $B$ field. For a particular choice of the involved parameters the action provides an alternative description of (complex) general relativity with a nonvanishing cosmological constant, whereas another choice corresponds to anti-self-dual gravity. Generic values of the parameters produce "close neighbors" of general relativity, although there is a peculiar choice of the parameters that leads to a Hamiltonian theory with two scalar constraints. Given the nontrivial form of the resulting scalar constraint for these models, we consider a more general setting where the scalar constraint is replaced with an arbitrary analytic function of some fundamental variables and show that the Poisson algebra involving this constraint together with the Gauss and vector constraints of the Ashtekar formalism closes, thus generating an infinite family of gravitational models that propagate the same number of degrees of freedom as general relativity.

Curved momentum spaces from quantum (anti–)de Sitter groups in ( 3+1 ) dimensions

Curved momentum spaces associated to the $\kappa$-deformation of the (3+1) de Sitter and Anti-de Sitter algebras are constructed as orbits of suitable actions of the dual Poisson-Lie group associated to the $\kappa$-deformation with non-vanishing cosmological constant. The $\kappa$-de Sitter and $\kappa$-Anti-de Sitter curved momentum spaces are separately analysed, and they turn out to be, respectively, half of the (6+1)-dimensional de Sitter space and half of a space with $SO(4,4)$ invariance. Such spaces are made of the momenta associated to spacetime translations and the "hyperbolic" momenta associated to boost transformations. The known $\kappa$-Poincar\'e curved momentum space is smoothly recovered as the vanishing cosmological constant limit from both of the constructions.

Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory.

A trajectory-based representation for the quantum theory of the gravitational field is formulated. This is achieved in terms of a covariant Generalized Lagrangian-Path (GLP) approach which relies on a suitable statistical representation of Bohmian Lagrangian trajectories, referred to here as GLP-representation. The result is established in the framework of the manifestly-covariant quantum gravity theory (CQG-theory) proposed recently and the related CQG-wave equation advancing in proper-time the quantum state associated with massive gravitons. Generally non-stationary analytical solutions for the CQG-wave equation with non-vanishing cosmological constant are determined in such a framework, which exhibit Gaussian-like probability densities that are non-dispersive in proper-time. As a remarkable outcome of the theory achieved by implementing these analytical solutions, the existence of an emergent gravity phenomenon is proven to hold. Accordingly, it is shown that a mean-field background space-time metric tensor can be expressed in terms of a suitable statistical average of stochastic fluctuations of the quantum gravitational field whose quantum-wave dynamics is described by GLP trajectories.

A Non-Polynomial Gravity Formulation for Loop Quantum Cosmology Bounce

Recently the so-called mimetic gravity approach has been used to obtain corrections to the Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via the so-called non-polynomial gravity approach, which consists of adding geometric non-polynomial higher derivative terms to Hilbert–Einstein action, which are nonetheless polynomials and lead to a second-order differential equation in Friedmann–Lemaître–Robertson–Walker space-times. Our explicit action turns out to be a realization of the Helling proposal of effective action with an infinite number of terms. The model is also investigated in the presence of a non-vanishing cosmological constant, and a new exact bounce solution is found and studied.