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Andronikos Paliathanasis

Publications and source records attributed to Andronikos Paliathanasis.

At least 253 records · Page 14Linked to original sources
arXiv2017

Group invariant transformations for the Klein-Gordon equation in three dimensional flat spaces

We perform the complete symmetry classification of the Klein-Gordon equation in maximal symmetric spacetimes. The central idea is to find all possible potential functions $V(t,x,y)$ that admit Lie and Noether symmetries. This is done by using the relation between the symmetry vectors of the differential equations and the elements of the conformal algebra of the underlying geometry. For some of the potentials, we use the admitted Lie algebras to determine corresponding invariant solutions to the Klein-Gordon equation. An integral part of this analysis is the problem of the classification of Lie and Noether point symmetries of the wave equation.

math-ph↗
arXiv2017

Noether symmetries and stability of ideal gas solution in Galileon Cosmology

A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether's Theorem to determine conservation laws for the field equations. In the Friedmann-Lemaître-Robertson-Walker universe, the existence of a nontrivial conservation law indicates the integrability of the field equations. Due to the complexity of the latter, we apply the differential invariants approach in order to construct special power-law solutions and study their stability.

gr-qc↗
arXiv2017

Symmetries and Singularities of the Szekeres System

The Szekeres system is studied with two methods for the determination of conservation laws. Specifically we apply the theory of group invariant transformations and the method of singularity analysis. We show that the Szekeres system admits a Lagrangian and the conservation laws that we find can be derived by the application of Noether's theorem. The stability for the special solutions of the Szekeres system is studied and it is related with the with the Left or Right Painlevé Series which describes the expansions.

gr-qc↗
arXiv2016

Exact solution of the Einstein-Skyrme model in a Kantowski-Sachs spacetime

We consider a Skyrme fluid with a constant radial profile in locally rotational Kantowski-Sachs spacetime. The Skyrme fluid is an anisotropic fluid with zero heat flux and with an equation of state parameter $w_{S}$ that $\left\vert w_{s}\right\vert \leq\frac{1}{3}$. From the Einstein field equations we define the Wheeler-DeWitt equation. For the last equation we perform a Lie symmetry classification and we determine the invariant solutions for the wavefunction of the model. Moreover from the Lie symmetries of the Wheeler-DeWitt equation we construct Noetherian conservation laws for the field equations which we use in order to write the solution in closed form. We show that all pf the cosmological parameters are expressed in terms of the scale factor of the two dimensional sphere of the Kantowski-Sachs spacetime. Finally from the application of Noether's theorem for the Wheeler-DeWitt equation we derive conservation laws for the wavefunction of the universe.

gr-qc↗
arXiv2016

Kantowski-Sachs Einstein-æther perfect fluid models

We investigate Kantowski-Sachs models in Einstein-æther theory with a perfect fluid source using the singularity analysis to prove the integrability of the field equations and dynamical system tools to study the evolution. We find an inflationary source at early times, and an inflationary sink at late times, for a wide region in the parameter space. The results by A. A. Coley, G. Leon, P. Sandin and J. Latta (JCAP 12, 010, 2015), are then re-obtained as particular cases. Additionally, we select other values for the non-GR parameters which are consistent with current constraints, getting a very rich phenomenology. In particular, we find solutions with infinite shear, zero curvature, and infinite matter energy density in comparison with the Hubble scalar. We also have stiff-like future attractors, anisotropic late-time attractors, or both, in some special cases. Such results are developed analytically, and then verified by numerics. Finally, the physical interpretation of the new critical points is discussed.

gr-qc↗
arXiv2016

Observational Constraints on New Exact Inflationary Scalar-field Solutions

An algorithm is used to generate new solutions of the scalar field equations in homogeneous and isotropic universes. Solutions can be found for pure scalar fields with various potentials in the absence and presence of spatial curvature and other perfect fluids. A series of generalisations of the Chaplygin gas and bulk viscous cosmological solutions for inflationary universes are found. Furthermore other closed-form solutions which provide inflationary universes are presented. We also show how the Hubble slow-roll parameters can be calculated using the solution algorithm and we compare these inflationary solutions with the observational data provided by the Planck 2015 collaboration in order to constraint and rule out some of these models.

gr-qc↗
arXiv2016

Noether symmetries and duality transformations in cosmology

We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian then there exists a coordinate system in which a reversal symmetry exists. Moreover as far as concerns the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular the same point symmetry as also the same reversal symmetry exists for the Brans-Dicke- scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans-Dicke parameter and it is a scale-factor duality when $ω_{BD}=1$. Furthermore, in the context of the O'Hanlon theory for $f\left( R\right) $-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.

gr-qc↗
arXiv2016

Noetherian symmetries of noncentral forces with drag term

We consider the Noetherian symmetries of second-order ODEs subjected to forces with nonzero curl. Both position and velocity dependent forces are considered. In the former case the first integrals are shown to follow from the symmetries of the celebrated Emden-Fowler equation.

math-ph↗
arXiv2016

Cosmological Solutions of $f(T)$ Gravity

In the cosmological scenario in $f\left( T\right) $ gravity, we find analytical solutions for an isotropic and homogeneous universe containing a dust fluid and radiation and for an empty anisotropic Bianchi I universe. The method that we apply is that of movable singularities of differential equations. For the isotropic universe, the solutions are expressed in terms of a Laurent expansion, while for the anisotropic universe we find a family of exact Kasner-like solutions in vacuum. Finally, we discuss when a nonlinear $f\left( T\right) $-gravity theory provides solutions for the teleparallel equivalence of general relativity and derive conditions for exact solutions of general relativity to solve the field equations of an $f(T)$ theory.

gr-qc↗
arXiv2016

Analytical solutions in $R+qR^{n}$ cosmology from singularity analysis

The integrability of higher-order theories of gravity is of importance in the determining the properties of these models and so their viability as models of reality. An important tool in the establishment of integrability is the singularity analysis. We apply this analysis to the case of fourth-order theory of gravity $f(R) = R + qR^{n}$ to establish those values of the free parameters $q$ and $n$ for which integrability in this sense exists. As a prelininary we examine the well-known case of $n = 4/3$.

gr-qc↗
arXiv2016

General Analytic Solutions of Scalar Field Cosmology with Arbitrary Potential

We present the solution space for the case of a minimally coupled scalar field with arbitrary potential in a FLRW metric. This is made possible due to the existence of a nonlocal integral of motion corresponding to the conformal Killing field of the two-dimensional minisuperspace metric. The case for both spatially flat and non flat are studied first in the presence of only the scalar field and subsequently with the addition of non interacting perfect fluids. It is verified that this addition does not change the general form of the solution, but only the particular expressions of the scalar field and the potential. The results are applied in the case of parametric dark energy models where we derive the scalar field equivalence solution for some proposed models in the literature.

gr-qc↗
arXiv2016

Evolution and Dynamics of a Matter creation model

In a flat Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) geometry, we consider the expansion of the universe powered by the gravitationally induced `adiabatic' matter creation. To demonstrate how matter creation works well with the expanding universe, we have considered a general creation rate and analyzed this rate in the framework of dynamical analysis. The dynamical analysis hints the presence of a non-singular universe (without the big bang singularity) with two successive accelerated phases, one at the very early phase of the universe (i.e. inflation), and the other one describes the current accelerating universe, where this early, late accelerated phases are associated with an unstable fixed point (i.e. repeller) and a stable fixed (attractor) points, respectively. We have described this phenomena by analytic solutions of the Hubble function and the scale factor of the FLRW universe. Using Jacobi Last multiplier method, we have found a Lagrangian for this matter creation rate describing this scenario of the universe. To match with our early physics results, we introduce an equivalent dynamics driven by a single scalar field and discussed the associated observable parameters compared them with the latest PLANCK data sets. Finally, introducing the teleparallel modified gravity, we have established an equivalent gravitational theory in the framework of matter creation.

gr-qc↗
arXiv2016

Comment on "A study of phantom scalar field cosmology using Lie and Noether symmetries" [Int. J. Mod. Phys. D 25 (2016) 1650051]

We show that the recent results of \ [Int. J. Mod. Phys. D 25 (2016) 1650051] on the application of Lie/Noether symmetries in scalar field cosmology are well-known in the literature while the problem could have been solved easily under a coordinate transformation. That follows from the property, that the admitted group of invariant transformations of dynamical system is independent on the coordinate system.

gr-qc↗
arXiv2016

Lie and Noether point symmetries of a class of quasilinear systems of second-order differential equations

We study the Lie and Noether point symmetries of a class of systems of second-order differential equations with $n$ independent and $m$ dependent variables ($n\times m$ systems). We solve the symmetry conditions in a geometric way and determine the general form of the symmetry vector and of the Noetherian conservation laws. We prove that the point symmetries are generated by the collineations of two (pseudo)metrics, which are defined in the spaces of independent and dependent variables. We demonstrate the general results in two special cases (a) a system of $m$ coupled Laplace equations and (b) the Klein-Gordon equation of a particle in the context of Generalized Uncertainty Principle. In the second case we determine the complete invariant group of point transformations, and we apply the Lie invariants in order to find invariant solutions of the wave function for a spin-$0$ particle in the two dimensional hyperbolic space.

math.DG↗
arXiv2016

Classical and Quantum Solutions in Brans-Dicke Cosmology with a Perfect Fluid

We consider the application of group invariant transformations in order to constrain a flat isotropic and homogeneous cosmological model, containing of a Brans-Dicke scalar field and a perfect fluid with a constant equation of state parameter $w$, where the latter is not interacting with the scalar field in the gravitational action integral. The requirement that the Wheeler-DeWitt equation be invariant under one-parameter point transformations provides us with two families of power-law potentials for the Brans-Dicke field, in which the powers are functions of the Brans-Dicke parameter $ω_{BD}$ and the parameter $w$. The existence of the Lie symmetry in the Wheeler-DeWitt equation is equivalent to the existence of a conserved quantity in field equations and with oscillatory terms in the wavefunction of the universe. This enables us to solve the field equations. For a specific value of the conserved quantity, we find a closed-form solution for the Hubble factor, which is equivalent to a cosmological model in general relativity containing two perfect fluids. This provides us with different models for specific values of the parameters $ω_{BD},$ and $w$. Finally, the results hold for the specific case where the Brans-Dicke parameter $ω_{BD}$ is zero, that is, for the O'Hanlon massive dilaton theory, and consequently for $f\left( R\right) $ gravity in the metric formalism.

gr-qc↗
arXiv2016

$f(R)$-gravity from Killing Tensors

We consider $f\left(R\right) $-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of $f\left(R\right) $ and the field equations to be invariant under Lie-Bäcklund transformations which are linear in the momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether's Theorem. We find three new integrable $f\left(R\right) $ models, for which with the application of the conservation laws we reduce the field equations to a system of two first-order ordinary differential equations. For each model we study the evolution of the cosmological fluid. Where we find that for the one integrable model the cosmological fluid has an equation of state parameter, in which in the latter there is a linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder (CPL) parametric dark energy model.

gr-qc↗
arXiv2015

Closed-form solutions of the Wheeler-DeWitt equation in a scalar-vector field cosmological model by Lie symmetries

We apply as selection rule to determine the unknown functions of a cosmological model the existence of Lie point symmetries for the Wheeler-DeWitt equation of quantum gravity. Our cosmological setting consists of a flat Friedmann-Robertson-Walker metric having the scale factor $a(t)$, a scalar field with potential function $V(ϕ)$ minimally coupled to gravity and a vector field of its kinetic energy is coupled with the scalar field by a coupling function $f(ϕ)$. Then, the Lie symmetries of this dynamical system are investigated by utilizing the behavior of the corresponding minisuperspace under the infinitesimal generator of the desired symmetries. It is shown that by applying the Lie symmetry condition the form of the coupling function and also the scalar field potential function may be explicitly determined so that we are able to solve the Wheeler-DeWitt equation. Finally, we show how we can use the Lie symmetries in order to construct conservation laws and exact solutions for the field equations.

gr-qc↗