Cosmological Constant Term Research Articles

Dark matter from torsion in Friedmann cosmology

A cosmological model in an Einstein–Cartan framework endowed with torsion is studied. For a torsion function assumed to be proportional to Hubble expansion function, namely phi =-alpha H, the contribution of torsion function as a dark matter component is studied in two different approaches. In the first one, the total matter energy density is altered by torsion coupling alpha , giving rise to an effective dark matter and cosmological constant terms that reproduce quite well the flat cosmic concordance model. In the second approach, starting with just standard baryonic matter plus a cosmological constant term, it is obtained that the coupling of torsion with baryons and cosmological constant term naturally gives rise to a dark matter contribution, together a modified cosmological term. In this model the dark matter sector can be interpreted as an effective coupling of the torsion function with the ordinary baryonic matter and cosmological constant. Finally, it is shown that both models are totally compatible with recent cosmological data from Supernovae and Hubble parameter measurements.

Global dynamics for the Szekeres system with non-zero cosmological constant

The Szekeres system with cosmological constant term describes the evolution of the kinematic quantities for the Einstein field equations in dimension four. It is a Hamiltonian system (with Hamiltonian H ). We restrict the dynamics on each one of the level surfaces H = h with h ∈ R and using the Poincaré compactification on R 3 we analyze the global dynamics of the Szekeres system. It was known that the Szekeres system with cosmological constant term exhibits an attractor in the finite regime. Here we provide a new proof of the finite attractor and additionally we prove that also exhibits a repulsor in the finite regime, and that at infinity there is an attractor and a repulsor.

Global dynamics and evolution for the Szekeres system with nonzero cosmological constant term

The Szekeres system with cosmological constant term describes the evolution of the kinematic quantities for Einstein field equations in \({\mathbb {R}}^4\). In this study, we investigate the behavior of trajectories in the presence of cosmological constant. It has been shown that the Szekeres system is a Hamiltonian dynamical system. It admits at least two conservation laws, h and \(I_{0}\) which indicate the integrability of the Hamiltonian system. We solve the Hamilton–Jacobi equation, and we reduce the Szekeres system from \({\mathbb {R}}^4\) to an equivalent system defined in \({\mathbb {R}}^2\). Global dynamics are studied where we find that there exists an attractor in the finite regime only for positive valued cosmological constant and \(I_0<-2 .08\). Otherwise, trajectories reach infinity. For \(I_ {0}>0\) the origin of trajectories in \({\mathbb {R}}^2\) is also at infinity. Finally, we investigate the evolution of physical properties by using dimensionless variables different from that of Hubble-normalization conducing to a dynamical system in \({\mathbb {R}}^5\). We see that the attractor at the finite regime in \({\mathbb {R}}^5\) is related with the de Sitter universe for a positive cosmological constant.

Lorentzian wormholes supported by tachyon matter

Wormholes with Ellis geometry have been successfully constructed using tachyon matter (Das and Kar, 2005). However, for such a wormhole, it is obtained that the redshift function is necessarily a constant, and also the wormhole is plagued with an imaginary tachyon potential and a constant field if the solutions are obtained in the absence of a cosmological constant term. So, a physically plausible wormhole solution is possible only in the presence of a Λ term. In this paper, we try to construct a wormhole from tachyon matter with three other geometries different from the Ellis geometry and see whether it is possible to construct them successfully, besides checking whether the restrictions of the Ellis wormhole can be overcome with these geometries. Among others, we obtain one very interesting result that for all three of these geometries different from the Ellis, the Λ term is no longer an essential ingredient in constructing physically plausible traversable wormholes and the tachyon matter, capable of providing explanations for the “dark sector” of the universe, is itself sufficient for this purpose.

Study on cosmic evolution and dynamics of a flat FLRW matter-dominated universe with a specified form of dynamical Cosmological Constant term

We have investigated a cosmological model of matter-dominated universe with a specified form of dynamic cosmological Λ-term, varying as Λ = lH + (l + λ) H2 + ½ηρ where l, λ and η are constants. We study the aforesaid cosmological model as an explanation for the accelerated expansion of the universe and obtain constraints on various model parameters for the estimation of the present values of cosmological parameters e.g.deceleration parameter, equation of state parameter, age of the universe. We also investigate the statefinder parameter {r, s}. In order to investigate stability of the system, we have treated the system in terms of dynamical system theory and studied dynamical properties and investigated critical points. By performing corresponding critical points analysis we have investigated different eras in the course of evolution of the universe.

Physical interpretation of Newman-Janis rotating systems. I. A unique family of Kerr-Schild systems

The Newman-Janis algorithm and its generalizations can be used mathematically to generate rotating solutions from nonrotating spherically-symmetric solutions within general relativity. The energy-momentum tensors of these solutions may or may not represent the same physical system, in the sense of both being a perfect fluid, or an electromagnetic field, or a $\Lambda$-term, and so on. In a series of two papers, we compare the structure of the eigenvalues and eigenvectors of the rotating and nonrotating energy-momentum tensors (their Segre types) and look for the existence of equations of state relating the energy density and the principal pressures. Part I covers Kerr-Schild systems, Part II more general systems. We find that there is a unique family of stationary axisymmetric Kerr-Schild systems that obey the same equation of state in both the rotating and nonrotating configurations. This family includes the Kerr and Kerr-Newman black holes, as well as rotating spacetimes whose mass function in the nonrotating limit contains a constrained superposition of a cloud of strings term, a Reissner-Nordstrom term, a cosmological constant term, and a Schwarzschild term. We describe the common equation of state relating energy density and pressure in this family of spacetimes and discuss some of its properties.

Modified amplitude of boson star rotation by the cosmological constant and coupling term of the curvature of the Universe

Modified amplitude of boson star rotation by the cosmological constant and coupling term of the curvature of the Universe

F(T) cosmology with nonzero curvature

We investigate exact and analytic solutions in [Formula: see text] gravity within the context of a Friedmann–Lemaître–Robertson–Walker background space with nonzero spatial curvature. For the power-law theory [Formula: see text] we find that the field equations admit an exact solution with a linear scalar factor for negative and positive spatial curvature. That Milne-like solution is asymptotic behavior for the scale factor near the initial singularity for the model [Formula: see text]. The analytic solution for that specific theory is presented in terms of Painlevé series for [Formula: see text]. Moreover, from the value of the resonances of the Painlevé series we conclude that the Milne-like solution is always unstable while for large values of the independent parameter, the field equations provide an expanding universe with a de Sitter expansion of a positive cosmological constant. Finally, the presence of the cosmological term [Formula: see text] in the studied [Formula: see text] model plays no role in the general behavior of the cosmological solution and the universe immerge in a de Sitter expansion either when the cosmological constant term [Formula: see text] in the [Formula: see text] model vanishes.

Charged BTZ-type solutions in Eddington-inspired Born-Infeld gravity

We construct an axially symmetric solution of Eddington-inspired Born-Infeld gravity coupled to an electromagnetic field in 2+1 dimensions including a (negative) cosmological constant term. This is achieved by using a recently developed mapping procedure that allows to generate solutions in certain families of metric-affine gravity theories starting from a known seed solution of General Relativity, which in the present case corresponds to the electrically charged Banados-Teitelboim-Zanelli (BTZ) solution. We discuss the main features of the new configurations, including the modifications to the ergospheres and horizons, the emergence of wormhole structures, and the consequences for the regularity (or not) of these space-times via geodesic completeness.

Maxwell-modified metric affine gravity

We present a gauge formulation of the special affine algebra extended to include an antisymmetric tensorial generator belonging to the tensor representation of the special linear group. We then obtain a Maxwell modified metric affine gravity action with a cosmological constant term. We find the field equations of the theory and show that the theory reduces to an Einstein-like equation for metric affine gravity with the source added to the gravity equations with cosmological constant mu contains linear contributions from the new gauge fields. The reduction of the Maxwell metric affine gravity to Riemann–Cartan one is discussed and the shear curvature tensor corresponding to the symmetric part of the special linear connection is identified with the dark energy. Furthermore, the new gauge fields are interpreted as geometrical inflaton vector fields which drive accelerated expansion.

Cosmological constraints on scalar field dark matter

This paper aims to put constraints on the parameters of the Scalar Field Dark Matter (SFDM) model, when dark matter is described by a free real scalar field filling the whole universe, plus a cosmological constant term. By using a compilation of 51 [Formula: see text] data and 1048 Supernovae data from Panteon, a mass range for the scalar field was obtained, [Formula: see text]eV, in good agreement with light mass axion particles. Also, we have obtained [Formula: see text], and the present dark matter density parameter [Formula: see text] at [Formula: see text] confidence level. These results are in good agreement to standard model of cosmology, showing that SFDM model is viable in describing the dark matter content of the universe.

Quantization of inhomogeneous spacetimes with cosmological constant term

We show that the Szekeres system with cosmological constant admits a sufficient number of conservation laws, which allow to claim the integrability of the system. The main novelty in this investigation is that we find that the unique attractor of the Szekeres system is the isotropic inhomogeneous de Sitter (-like) Universe, contrary to the original system in which the attractors describe Kantowski–Sachs (-like) spacetimes. We also study the existence of quantum corrections and the emergence of classicality by considering the linear and quadratic conserved quantities at the quantum level. We perform an analysis considering different approaches, involving the Bohmian quantum potential and a probability analysis. The result is that there are no quantum corrections for the quadratic integrals, while there exists a linear case for which we find quantum corrections.

New class of exact solutions to Einstein\u2013Maxwell-dilaton theory on four-dimensional Bianchi type IX geometry

We construct new classes of cosmological solution to the five dimensional Einstein–Maxwell-dilaton theory, that are non-stationary and almost conformally regular everywhere. The base geometry for the solutions is the four-dimensional Bianchi type IX geometry. In the theory, the dilaton field is coupled to the electromagnetic field and the cosmological constant term, with two different coupling constants. We consider all possible solutions with different values of the coupling constants, where the cosmological constant takes any positive, negative or zero values. In the ansatzes for the metric, dilaton and electromagnetic fields, we consider dependence on time and two spatial directions. We also consider a special case of the Bianchi type IX geometry, in which the geometry reduces to that of Eguchi–Hanson type II geometry and find a more general solution to the theory.

Corners of gravity: the case of gravity as a constrained BF theory

Following recent works on corner charges we investigate the boundary structure in the case of the theory of gravity formulated as a constrained BF theory. This allows us not only to introduce the cosmological constant, but also explore the influence of the topological terms present in the action of this theory. Established formulas for charges resemble previously obtained ones, but we show that they are affected by the presence of the cosmological constant and topological terms. As an example we discuss the charges in the case of the AdS-Schwarzschild solution and we find that the charges give correct values.

Symplectic Quantization II: Dynamics of Space\u2013Time Quantum Fluctuations and the Cosmological Constant

The symplectic quantization scheme proposed for matter scalar fields in the companion paper (Gradenigo and Livi, arXiv:2101.02125, 2021) is generalized here to the case of space–time quantum fluctuations. That is, we present a new formalism to frame the quantum gravity problem. Inspired by the stochastic quantization approach to gravity, symplectic quantization considers an explicit dependence of the metric tensor g_{mu nu } on an additional time variable, named intrinsic time at variance with the coordinate time of relativity, from which it is different. The physical meaning of intrinsic time, which is truly a parameter and not a coordinate, is to label the sequence of g_{mu nu } quantum fluctuations at a given point of the four-dimensional space–time continuum. For this reason symplectic quantization necessarily incorporates a new degree of freedom, the derivative {dot{g}}_{mu nu } of the metric field with respect to intrinsic time, corresponding to the conjugated momentum pi _{mu nu }. Our proposal is to describe the quantum fluctuations of gravity by means of a symplectic dynamics generated by a generalized action functional {mathcal {A}}[g_{mu nu },pi _{mu nu }] = {mathcal {K}}[g_{mu nu },pi _{mu nu }] - S[g_{mu nu }], playing formally the role of a Hamilton function, where S[g_{mu nu }] is the standard Einstein–Hilbert action while {mathcal {K}}[g_{mu nu },pi _{mu nu }] is a new term including the kinetic degrees of freedom of the field. Such an action allows us to define an ensemble for the quantum fluctuations of g_{mu nu } analogous to the microcanonical one in statistical mechanics, with the only difference that in the present case one has conservation of the generalized action {mathcal {A}}[g_{mu nu },pi _{mu nu }] and not of energy. Since the Einstein–Hilbert action S[g_{mu nu }] plays the role of a potential term in the new pseudo-Hamiltonian formalism, it can fluctuate along the symplectic action-preserving dynamics. These fluctuations are the quantum fluctuations of g_{mu nu }. Finally, we show how the standard path-integral approach to gravity can be obtained as an approximation of the symplectic quantization approach. By doing so we explain how the integration over the conjugated momentum field pi _{mu nu } gives rise to a cosmological constant term in the path-integral approach.

Gauge theory formulation of hyperbolic gravity

We formulate the most general gravitational models with constant negative curvature (“hyperbolic gravity”) on an arbitrary orientable two-dimensional surface of genus g with b circle boundaries in terms of a PSL(2, ℝ)∂ gauge theory of flat connections. This includes the usual JT gravity with Dirichlet boundary conditions for the dilaton field as a special case. A key ingredient is to realize that the correct gauge group is not the full PSL(2, ℝ), but a subgroup PSL(2, ℝ)∂ of gauge transformations that go to U(1) local rotations on the boundary. We find four possible classes of boundary conditions, with associated boundary terms, that can be applied to each boundary component independently. Class I has five inequivalent variants, corresponding to geodesic boundaries of fixed length, cusps, conical defects of fixed angle or large cylinder-shaped asymptotic regions with boundaries of fixed lengths and extrinsic curvatures one or greater than one. Class II precisely reproduces the usual JT gravity. In particular, the crucial extrinsic curvature boundary term of the usual second order formulation is automatically generated by the gauge theory boundary term. Class III is a more exotic possibility for which the integrated extrinsic curvature is fixed on the boundary. Class IV is the Legendre transform of class II; the constraint of fixed length is replaced by a boundary cosmological constant term.

Early Universe in view of a modified theory of gravity

We study the quantum evolution of the early Universe, its semi-classical analogue together with inflationary regime, in view of a generalized modified theory of gravity. The action is built by supplementing the non-minimally coupled scalar–tensor theory of gravity with scalar curvature squared term and a Gauss–Bonnet-dilatonic coupled term. It is generalized, since all the parameters are treated as arbitrary functions of the scalar field. It is interesting to explore the fact that instead of considering additional flow parameters, an effective potential serves the purpose of finding inflationary parameters. The dilaton stabilization issue appears here as a problem with reheating. Addition of a cosmological constant term alleviates the problem, and inflation is effectively driven by the vacuum energy density. Thus Gauss–Bonnet term might play a significant role in describing late-time cosmic evolution.

Quantum dynamics of the corner of the Bianchi IX model in the WKB approximation

In this paper we analyse the Bianchi IX Universe dynamics within the corner region associated to the potential term which the spatial curvature induces in the Minisuperspace. The study is done in the vacuum and in the presence of a massless scalar field $\phi$ and a cosmological constant term $\Lambda$. We investigate the dynamics in terms of WKB scenario for which the isotropic Misner variables (the volume) and one of the two anisotropic ones (and $\phi$ when present) are treated on a semi-classical level, while the remaining anisotropy degree of freedom, the one trapped in the corner, is described on a pure quantum level. The quantum dynamics always reduces to the one of a time-dependent Schr\"{o}edinger equation for a harmonic potential with a time dependent frequency. The vacuum case is treated in the limits of a collpasing and an expanding Universe, while the dynamics in presence of $\phi$ and $\Lambda$ is studied for $t \rightarrow \infty $. In both analysis the quantum dynamics of the anisotropy variable is associated to a decaying standard deviation of its probability density, corresponding to a suppression of the quantum anisotropy associated. In the vacuum case, the corner configuration becomes an attractor for the dynamics and the evolution resembles that one of a Taub cosmology in the limit of a non-singular initial Universe. This suggests that if the Bianchi dynamics enters enough the potential corner then the initial singularity is removed and a Taub picture emerges. The case when $\phi$ is present well mimics the De-Sitter phase of an inflationary Universe. Here we show that both the classical and quantum anisotropies are exponentially suppressed, so that the resulting dynamics corresponds to an isotropic closed Robertson-Walker geometry.

Specific entropy as a clock for the evolutionary quantization of the isotropic Universe

In this paper, we analyze the dynamics of an isotropic closed Universe in presence of a cosmological constant term and we compare its behavior in the standard Wheeler–DeWitt equation approach with the one when a Lagrangian fluid is considered in the spirit of the Kuchar–Brown paradigm. In particular, we compare the tunnelling of the Universe from the classically forbidden region to the allowed one, showing that considering a time evolution deeply influences the nature of the model. In fact, we show that in the presence of the Lagrangian fluid, the cosmological singularity is restored both in the classical and the quantum regime. However, in the quantum regime the singularity is probabilistically suppressed for some energy eigenvalues and in the case the latter is equal to zero one recovers the standard WDW case. Finally, we introduce a cut-off physics feature in the Minisuperspace by considering a Polymer quantum mechanical approach limiting our attention to the semi-classical dynamics mainly (the quantum treatment is inhibited by the non-local nature of the Hamiltonian operator). We show that the singularity is again removed, like in the fluid-free model, and a bouncing cosmology emerges so that the present model could mimic a cyclic cosmology.

Infinite dimensional symmetry groups of the Friedmann equations

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.