arXiv subjects

Andronikos Paliathanasis

Publications and source records attributed to Andronikos Paliathanasis.

At least 145 records · Page 8Linked to original sources

arXiv2021

Interacting quintessence in light of Generalized Uncertainty Principle: Cosmological perturbations and dynamics

We consider a cosmological scenario endowed with an interaction between the universe's dark components $-$ dark matter and dark energy. Specifically, we assume the dark matter component to be a pressure-less fluid, while the dark energy component is a quintessence scalar field with Lagrangian function modified by the quadratic Generalized Uncertainty Principle. The latter modification introduces new higher-order terms of fourth-derivative due to quantum corrections in the scalar field's equation of motion. Then we investigate asymptotic dynamics and general behaviour of solutions of the field equations for some interacting models of special interests in the literature. At the background level, the present interacting model exhibits the matter-dominated and de Sitter solutions which are absent in the corresponding quintessence model. Furthermore, to boost the background analysis, we study cosmological linear perturbations in the Newtonian gauge where we show how perturbations are modified by quantum corrected terms from the quadratic Generalized Uncertainty Principle. Depending on the coupling parameters, scalar perturbations show a wide range of behavior.

gr-qc↗

arXiv2021

Einstein-æther Scalar-tensor Cosmology

We propose an Einstein-æther scalar-tensor cosmological model. In particular in the scalar-tensor Action Integral we introduce the æther field with æther coefficients to be functions of the scalar field. This cosmological model extends previous studies on Lorentz-violating theories. For a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker background space we write the field equations which are of second-order with dynamical variables the scale factor and the scalar field. The physical evolution of the field equations depends upon three unknown functions which are related to the scalar-tensor coupling function, the scalar field potential and the æther coefficient functions. We investigate the existence of analytic solutions for the field equations and the integrability properties according to the existence of linear in the momentum conservation laws. We define a new set of variables in which the dynamical evolution depends only upon the scalar field potential. Furthermore, the asymptotic behaviour and the cosmological history is investigated where we find that the theory provides inflationary eras similar with that of scalar-tensor theory but with Lorentz-violating terms provided by the æther field. Finally, in the new variables we found that the field equations are integrable due to the existence of nonlocal conservation laws for arbitrary functional forms of the three free functions.

gr-qc↗

arXiv2021

Dynamics in interacting scalar-torsion theory

In a spatially flat \ Friedmann--Lema\^ıtre--Robertson--Walker background space we consider a scalar-torsion gravitational model which has similar properties with the dilaton theory. This teleparallel model is invariant under a discrete transformation similar to the Gasperini-Veneziano duality transformation. Moreover, in the gravitational Action integral we introduce the Lagrangian function of a pressureless fluid source which is coupled to the teleparallel dilaton field. This specific gravitational theory with interaction in the dark sector of the universe is investigated by using methods of the dynamical system analysis. We calculate that the theory provides various areas of special interest for the evolution of the cosmological history. Inflationary scaling solutions and the de Sitter universe is recovered. Furthermore, we calculate that there exist an attractor which provides a stable solution where the two fluid components, the scalar field and the pressureless matter, contribute in the cosmological fluid. This solution is of special interest because it can describe the present epoch. Finally, the qualitative evolution of the cosmographic parameters is discussed.

gr-qc↗

arXiv2021

Symmetry analysis for the $2+1$ generalized quantum Zakharov-Kuznetsov equation

We solve the group classification problem for the $2+1$ generalized quantum Zakharov-Kuznetsov equation. Particularly we consider the generalized equation $u_{t}+f\left( u\right) u_{z}+u_{zzz}+u_{xxz}=0$, and the time-dependent Zakharov-Kuznetsov equation $u_{t}+δ\left( t\right) uu_{z}+λ\left( t\right) u_{zzz}+\varepsilon \left( t\right) u_{xxz}=0$% . Function $f\left( u\right) $ and $δ\left( t\right) ,~λ\left( t\right) $,~$\varepsilon \left( t\right) $ are determine in order the equations to admit additional Lie symmetries.\ Finally, we apply the Lie invariants to find similarity solutions for the generalized quantum Zakharov-Kuznetsov equation.

math-ph↗

arXiv2021

$f(T)$ Cosmology with Nonzero Curvature

We investigate exact and analytic solutions in $f\left( T\right) $ gravity within the context of a Friedmann--Lema\^ıtre--Robertson--Walker background space with nonzero spatial curvature. For the power law theory $f\left( T\right) =T^{n}$ 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 behaviour for the scale factor near the initial singularity for the model $f\left( T\right) =T+f_{0}T^{n}-2Λ$. The analytic solution for that specific theory is presented in terms of Painlevé Series for $n>1$. 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 indepedent 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 $Λ$ in the studied $f\left( T\right) $ 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 $Λ$ in the $f\left( T\right) $ model vanishes.

gr-qc↗

arXiv2021

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.

gr-qc↗

arXiv2021

$O(d,d)$ symmetry in teleparallel dark energy

An important characteristic of the Dilaton cosmological model is the Gasperini-Veneziano duality transformation which follows from the existence of the $O\left( d,d\right) $ symmetry. In this study, we consider the equivalent Dilaton theory in teleparallel dark energy with the $O\left( d,d\right) $ symmetry, while the equivalent teleparallel-duality transformation is presented. The classical solution of the field equations is derived. Finally the Wheeler-DeWitt equation of quantum cosmology is discussed.

gr-qc↗

arXiv2021

Projective collineations of decomposable spacetimes generated by the Lie point symmetries of geodesic equations

We investigate the relation of the Lie point symmetries for the geodesic equations with the collineations of decomposable spacetimes. We review previous results in the literature on the Lie point symmetries of the geodesic equations and we follow a previous proposed geometric construction approach for the symmetries of differential equations. In this study we prove that the projective collineations of a $\left( n+1\right) \,$% -dimensional decomposable Riemannian space are the Lie point symmetries for geodesic equations of the $n$-dimensional subspace. We demonstrate the application of our results with the presentation of applications.

gr-qc↗

arXiv2021

Cosmological evolution in $f(T,B)$ gravity

For the fourth-order teleparallel $f\left(T,B\right) $ theory of gravity, we investigate the cosmological evolution for the universe in the case of a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker background space. We focus on the case for which $f\left(T,B\right) $ is separable, that is, $f\left(T,B\right) _{,TB}=0$ and $f\left(T,B\right) $ is a nonlinear function on the scalars $T$ and $B$. For this fourth-order theory we use a Lagrange multiplier to introduce a scalar field function which attributes the higher-order derivatives. In order to perform the analysis of the dynamics we use dimensionless variables which allow the Hubble function to change sign. The stationary points of the dynamical system are investigated both in the finite and infinite regimes. The physical properties of the asymptotic solutions and their stability characteristics are discussed.

gr-qc↗

arXiv2021

$\mathcal{N}$-field cosmology in hyperbolic field space: stability and general solutions

We study the dynamics of a cosmological model with a perfect fluid and $\mathcal{N}$ fields on a hyperbolic field space interacting via a symmetric potential. We list all late-time solutions, investigate their stability and briefly discuss predictions of the theory. Moreover, for the case of two scalar fields and an exponential potential we prove that the field equations are Liouville integrable and we provide for the first time the general solution for a region of the parameter space.

gr-qc↗

arXiv2021

Cosmological solutions and growth index of matter perturbations in $f(Q)$ gravity

The present work studies one of Einstein's alternative formulations based on the non-metricity scalar $Q$ generalized as $f(Q)$ theory. More specifically, we consider the power-law form of $f(Q)$ gravity i.e. $f(Q)=Q+α\, Q^n$. Here, we analyze the behavior of the cosmological model at the background and perturbation level. At the background level, we find the effective evolution of the model is the same as that of the $Λ$CDM for $|n|<1$. Interestingly, the geometric component of the theory solely determined the late-time acceleration of the Universe. We also examine the integrability of the model by employing the method of singularity analysis. In particular, we find the conditions under which field equations pass the Painlevé test and hence possess the Painlevé property. While the equations pass the Painlevé test in the presence of dust for any value of $n$, the test is valid after the addition of radiation fluid only for $n<1$. Finally, at the perturbation level, the behavior of matter growth index signifies a deviation of the model from the $Λ$CDM even for $|n|<1$.

gr-qc↗

arXiv2021

Exact Anti-Self-Dual four-manifolds with a Killing symmetry by similarity transformations

We study the group properties and the similarity solutions for the constraint conditions of anti-self-dual null Kähler four-dimensional manifolds with at least a Killing symmetry vector. Specifically we apply the theory of Lie symmetries to determine all the infinitesimal generators of the one-parameter point transformations which leave the system invariant. We use these transformations to define invariant similarity transformations which are used to simplify the differential equations and find the exact form of the spacetime. We show that the constraint equations admit an infinite number of symmetries which can be used to construct an infinite number of similarity transformations.

gr-qc↗

arXiv2021

Similarity solutions for two-phase fluids models

The algebraic properties of drift-flux two-phase fluids models without gravitational and wall friction forces are studied. More precisely, for the two fluids we consider equation of states of polytropic gases. We perform a classification scheme of the unknown parameters of the model such that to determine all the possible admitted Lie symmetries. We find that in the most general case the dynamical system of hyperbolic equations is invariant under the action of a four dimensional Lie algebra, while the larger number of admitted Lie symmetries is six. For each admitted Lie algebra the one-dimensional optimal system is derived which is applied for the determination of all the unique similarity transformations which lead to similarity solutions. Our results are compared with that of previous studies from where we see that most of the solutions presented in this study have not found before in the literature.

physics.flu-dyn↗

arXiv2021

Group properties and solutions for the 1D Hall MHD system in the cold plasma approximation

We study the Lie point symmetries and the similarity transformations for the partial differential equations of the nonlinear one-dimensional magnetohydrodynamic system with the Hall term known as HMHD system. For this 1+1 system of partial differential equations we find that is invariant under the action of a seventh dimensional Lie algebra. Furthermore, the one-dimensional optimal system is derived while the Lie invariants are applied for the derivation of similarity transformations. We present different kinds of oscillating solutions.

physics.plasm-ph↗

arXiv2021

Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations

We apply the theory of infinitesimal transformations for the study of a family of 1+1 fifth-order partial differential equations which have been proposed before for the description of multiple kink solutions. In this analysis we perform a complete classification of the Lie symmetries and of the one-dimensional optimal system. The results are applied for the derivation of similarity solutions and in particular we find travel-wave and scaling solutions. We show that the kink-solution of these equations can be recovered by the use of the Lie symmetries, while new solutions are also derived.

nlin.SI↗

arXiv2021

New conservation laws and exact cosmological solutions in Brans-Dicke cosmology with an extra scalar field

The derivation of conservation laws and invariant functions is an essential procedure for the investigation of nonlinear dynamical systems. In this study we consider a two-field cosmological model with scalar fields defined in the Jordan frame. In particular we consider a Brans-Dicke scalar field theory and for the second scalar field we consider a quintessence scalar field minimally coupled to gravity. For this cosmological model we apply for the first time a new technique for the derivation of conservation laws without the application of variational symmetries. The results are applied for the derivation of new exact solutions. The stability properties of the scaling solutions are investigated and criteria for the nature of the second field according to the stability of these solutions are determined.

gr-qc↗

arXiv2021

Variational symmetries and superintegrability in multifield cosmology

We consider a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker background space with an ideal gas and a multifield Lagrangian consisting of two minimally coupled scalar fields which evolve in a field space of constant curvature. For this cosmological model we classify the potential function for the scalar fields such that variational point symmetries exist. The corresponding conservation laws are calculated. Finally, analytic solutions are presented for specific functional forms of the scalar field potential in which the cosmological field equations are characterized as a Liouville integrable system by point symmetries. The free parameters of the cosmological model are constrained in order to describe analytic solutions for an inflationary epoch. Finally, stability properties of exact closed-form solutions are investigated. These solutions are scaling solutions with important physical properties for the cosmological model.

gr-qc↗

arXiv2021

Minisuperspace Quantization of $f\left(T,B\right) $ Cosmology

We discuss the quantization in the minisuperspace for the generalized fourth-order teleparallel cosmological theory known as $f\left( T,B\right) $. Specifically we focus on the case where the theory is linear on the torsion scalar, in that consideration we are able to write the cosmological field equations with the use of a scalar field different from the scalar tensor theories, but with the same dynamical constraints as that of scalar tensor theories. We use the minisuperspace description to write for the first time the Wheeler-DeWitt equation. With the use of the theory of similarity transformations we are able to find exact solutions for the Wheeler-DeWitt equations as also to investigate the classical and semiclassical limit in the de Broglie -Bohm representation of quantum mechanics.

gr-qc↗