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Andronikos Paliathanasis

Publications and source records attributed to Andronikos Paliathanasis.

At least 235 records · Page 13Linked to original sources
arXiv2018

Latest astronomical constraints on some nonlinear parametric dark energy models

We consider nonlinear redshift-dependent equation of state parameters as dark energy models in a spatially flat Friedmann-Lemaître-Robertson-Walker universe. To depict the expansion history of the universe in such cosmological scenarios, we take into account the large scale behaviour of such parametric models and fit them using a set of latest observational data with distinct origin that includes cosmic microwave background radiation, Supernove Type Ia, baryon acoustic oscillations, redshift space distortion, weak gravitational lensing, Hubble parameter measurements from cosmic chronometers and finally the local Hubble constant from Hubble space telescope. The fitting technique avails the publicly available code Cosmological Monte Carlo (CosmoMC), to extract the cosmological information out of these parametric dark energy models. From our analysis it follows that those models could describe the late time accelerating phase of the universe, while they are distinguished from the $Λ-$cosmology.

gr-qc↗
arXiv2018

Nonlocal Representation of the $sl(2,R)$ Algebra for the Chazy equation

A demonstration of how the point symmetries of the Chazy Equation become nonlocal symmetries for the reduced equation is discussed. Moreover we construct an equivalent third-order differential equation which is related to the Chazy Equation under a generalized transformation, and find the point symmetries of the Chazy Equation are generalized symmetries for the new equation. With the use of singularity analysis and a simple coordinate transformation we construct a solution for the Chazy Equation which is given by a Right Painlevé Series. The singularity analysis is applied to the new third-order equation and we find that it admits two solutions, one given by a Left Painlevé Series and one given by a Right Painlevé Series where the leading-order behaviors and the resonances are explicitly those of the Chazy Equation.

math.CA↗
arXiv2018

Stability of the Kasner Universe in f(T) Gravity

$f(T)$ gravity offers an alternative context in which to consider gravitational interactions where torsion, rather than curvature, is the mechanism by which gravitation is communicated. We investigate the stability of the Kasner solution with several forms of the arbitrary lagrangian function examined within the $f(T)$ context. This is a Bianchi type--I vacuum solution with anisotropic expansion factors. In the $f(T)$ gravity setting, the solution must conform to a set of conditions in order to continue to be a vacuum solution of the generalized field equations. With this solution in hand, the perturbed field equations are determined for power-law and exponential forms of the $f(T)$ function. We find that the point which describes the Kasner solution is a saddle point which means that the singular solution is unstable. However, we find the de Sitter universe is a late-time attractor. In general relativity, the cosmological constant drives the the isotropization of the spacetime while in this setting the extra $f(T)$ contributions now provide this impetus.

gr-qc↗
arXiv2017

(Compactified) black branes in four dimensional f(R)-gravity

A new family of analytical solutions in a four dimensional static spacetime is presented for $f\left( R\right) $-gravity. In contrast to General Relativity, we find that a non trivial black string/ring solution is supported in vacuum power law $f\left( R\right) $-gravity for appropriate values of the parameters characterizing the model and when axisymmetry is introduced in the line element. For the aforementioned solution, we perform a brief investigation over its basic thermodynamic quantities.

gr-qc↗
arXiv2017

Approximate Noether Symmetries and Collineations for Regular Perturbative Lagrangians

Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying manifold. In particular we determine the generic Noether symmetry conditions for the approximate point symmetries and we find that for a class of perturbed Lagrangians, Noether symmetries are related to the elements of the Homothetic algebra of the metric which is defined by the unperturbed Lagrangian. Moreover, we discuss how exact symmetries become approximate symmetries. Finally, some applications are presented.

math-ph↗
arXiv2017

Lie symmetries for systems of evolution equations

The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined

math.AP↗
arXiv2017

de Sitter and Scaling solutions in a higher-order modified teleparallel theory

The existence and the stability conditions for some exact relativistic solutions of special interest are studied in a higher-order modified teleparallel gravitational theory. The theory with the use of a Lagrange multiplier is equivalent with that of General Relativity with a minimally coupled noncanonical field. The conditions for the existence of de Sitter solutions and ideal gas solutions in the case of vacuum are studied as also the stability criteria. Furthermore, in the presence of matter the behaviour of scaling solutions is given. Finally, we discuss the degrees of freedom of the field equations and we reduce the field equations in an algebraic equation, where in order to demonstrate our result we show how this noncanonical scalar field can reproduce the Hubble function of $Λ$-cosmology.

gr-qc↗
arXiv2017

Lie and Noether point Symmetries for a Class of Nonautonomous Dynamical Systems

We prove two general theorems which determine the Lie and the Noether point symmetries for the equations of motion of a dynamical system which moves in a general Riemannian space under the action of a time dependent potential $W(t,x)=ω(t)V(x)$. We apply the theorems to the case of a time dependent central potential and the harmonic oscillator and determine all Lie and Noether point symmetries. Finally we prove that these theorems also apply to the case of a dynamical system with linear dumping and study two examples.

math.CA↗
arXiv2017

Topologically non-trivial configurations in the 4d Einstein--nonlinear $σ$-model system

We construct exact, regular and topologically non-trivial\ configurations of the coupled Einstein-nonlinear sigma model in (3+1) dimensions. The ansatz for the nonlinear $SU(2)$ field is regular everywhere and circumvents Derrick's theorem because it depends explicitly on time, but in such a way that its energy-momentum tensor is compatible with a stationary metric. Moreover, the $SU(2)$ configuration cannot be continuously deformed to the trivial Pion vacuum as it possesses a non-trivial winding number. We reduce the full coupled 4D Einstein nonlinear sigma model system to a single second order ordinary differential equation. When the cosmological constant vanishes, such master equation can be further reduced to an Abel equation. Two interesting regular solutions correspond to a stationary traversable wormhole (whose only \textquotedblleft exotic matter" is a negative cosmological constant) and a (3+1)-dimensional cylinder whose (2+1)-dimensional section is a Lorentzian squashed sphere. The Klein-Gordon equation in these two families of spacetimes can be solved in terms of special functions. The angular equation gives rise to the Jacobi polynomials while the radial equation belongs to the Poschl-Teller family. The solvability of the Poschl-Teller problem implies non-trivial quantization conditions on the parameters of the theory.

hep-th↗
arXiv2017

Integrability from Point Symmetries in a family of Cosmological Horndeski Lagrangians

For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lema\^ıtre-Robertson-Walker spacetime. We are interested in point transformations which leave invariant the field equations. Noether's theorem is applied to determine the conservation laws for a family of models that belong to the same general class. The cosmological scenarios with or without an extra perfect fluid with constant equation of state parameter are the two important cases of our study. \ The De Sitter universe and ideal gas solutions are derived by using the invariant functions of the symmetry generators as a demonstration of our result. Furthermore, we discuss the connection of the different models under conformal transformations while we show that when the Horndeski theory reduces to a canonical field the same holds for the conformal equivalent theory. Finally we discuss how singular solutions provides nonsingular universes in a different frame and vice versa.

gr-qc↗
arXiv2017

Analytic Solution of the Starobinsky Model for Inflation

We prove that the field equations of the Starobinsky model for inflation in a Friedmann-Lema\^ıtre-Robertson-Walker constitute an integrable system as the field equations pass the singularity test. The analytical solution in terms of a Painlevé Series for the Starobinsky model is presented for the case of zero and nonzero spatial curvature. In both cases the leading-order term describes the radiation era provided by the corresponding higher-order theory.

gr-qc↗
arXiv2017

Dynamical Analysis of an Integrable Cubic Galileon Cosmological Model

Recently a cubic Galileon cosmological model was derived by the assumption that the field equations are invariant under the action of point transformations. The cubic Galileon model admits a second conservation law which means that the field equations form an integrable system. The analysis of the critical points for this integrable model is the main subject of this work. To perform the analysis, we work on dimensionless variables different from that of the Hubble normalization. New critical points are derived while the gravitational effects which follow from the cubic term are studied.

gr-qc↗
arXiv2017

Cosmological solutions with gravitational particle production and non-zero curvature

In a homogeneous and isotropic universe with non-zero spatial curvature we consider the effects of gravitational particle production in the dynamics of the universe. We show that the dynamics of the universe in such a background is characterized by a single nonlinear differential equation which is significantly dependent on the rate of particle creation and whose solutions can be dominated by the curvature effects at early times. For different particle creation rates we apply the singularity test in order to find the analytic solutions of the background dynamics. We describe the behavior of the cosmological solutions for both open and closed universes. We also show how the effects of curvature can be produced by the presence of a second perfect fluid with an appropriate equation of state. By combining that results with the analysis of the critical points we find that our consideration can be related with the pre-inflationary era. Specifically we find that for negative spatial curvature small changes of the Milne spacetime leads to a de Sitter universe.

gr-qc↗
arXiv2017

Cosmological Einstein-Skyrme solutions with non-vanishing topological charge

Time-dependent analytic solutions of the Einstein-Skyrme system --gravitating Skyrmions--, with topological charge one are analyzed in detail. In particular, the question of whether these Skyrmions reach a spherically symmetric configuration for $t\rightarrow+\infty$ is discussed. It is shown that there is a static, spherically symmetric solution described by the Ermakov-Pinney system, which is fully integrable by algebraic methods. For $Λ>0$ this spherically symmetric solution is found to be in a "neutral equilibrium" under small deformations, in the sense that under a small squashing it would neither blow up nor dissapear after a long time, but it would remain finite forever (plastic deformation). Thus, in a sense, the coupling with Einstein gravity spontaneously breaks the spherical symmetry of the solution. However, in spite of the lack of isotropy, for $t \to\infty$ (and $Λ>0$) the space time is locally flat and the anisotropy of the Skyrmion only reflects the squashing of spacetime.

hep-th↗
arXiv2017

Cosmological Evolution and Exact Solutions in a Fourth-order Theory of Gravity

A fourth-order theory of gravity is considered which in terms of dynamics has the same degrees of freedom and number of constraints as those of scalar-tensor theories. In addition it admits a canonical point-like Lagrangian description. We study the critical points of the theory and we show that it can describe the matter epoch of the universe and that two accelerated phases can be recovered one of which describes a de Sitter universe. Finally for some models exact solutions are presented.

gr-qc↗