arXiv subjects

Andronikos Paliathanasis

Publications and source records attributed to Andronikos Paliathanasis.

At least 73 records · Page 4Linked to original sources

arXiv2025

Testing an oscillatory behavior of dark energy

The main aim of this work is to use a model-independent approach, along with late-time observational probes, to reconstruct the dark energy (DE) equation of state $w_{\rm DE}(z)$. Our analysis showed that, for a late time universe, $w_{\rm DE}$ deviates from being a constant but in contrast exhibits an oscillatory behavior, hence both quintessence ($w_{\rm DE}> -1$) and phantom ($w_{\rm DE} < -1$) regimes are equally allowed. In order to portray this oscillatory behavior, we explored various parametrizations for the equation of state and identified the closest approximation based on the goodness of fit with the data and the Bayesian evidence analysis. Our findings indicated that while all considered oscillating DE parametrizations provided a better fit to the data, compared to the cosmological constant, they are penalized in the Bayesian evidence analysis due to the additional free parameters. Overall, the present article demonstrates that in the low redshift regime, the equation of state of the DE prefers to be dynamical and oscillating. We anticipate that future cosmological probes will take a stand in this direction.

astro-ph.CO↗

arXiv2025

Cosmological Solutions in Scalar-Tensor theory via the Eisenhart-Duval lift

We implement the Einsenhart-Duval lift in scalar-tensor gravity as a means to construct integrable cosmological models and analytic cosmological solutions. Specifically, we employ a geometric criterion to constrain the free functions of the scalar-tensor theory such that the field equations can be written in the equivalent form of linear equations. This geometric linearization is achieved by the introduction of an extended minisuperspace description. The results are applied to construct analytic solutions in modified theories of gravity such as the $f\left( R\right) $-theory and the hybrid metric-Palatini $f\left( \mathcal{R}\right) $-gravity.

gr-qc↗

arXiv2025

Cosmological Interactions with Phantom Scalar Field: Revisiting Background Phase-Space Analysis with Compactified Variables

Energy transfer in the dark sector of the universe gives rise to new phenomena of special interest in modern cosmology. When dark energy is modeled as a phantom scalar field, interactions become crucial to avoid Big Rip singularities. In this work, we revisit the phase-space analysis of the field equations by introducing a new set of dimensionless variables distinct from the traditional Hubble normalization approach. These new variables define a compactified phase space for the evolution of physical parameters. We demonstrate that these compactified variables offer fresh insights into the phase-space analysis in gravitational theories, particularly when the dark energy fluid is allowed to possess a negative kinetic energy density.

gr-qc↗

arXiv2024

Static, spherically symmetric solutions in $f(Q)$-gravity and in nonmetricity scalar-tensor theory

We solve the gravitational field equations for a static, spherically symmetric spacetime within the framework of the symmetric teleparallel theory of gravity. Specifically, we derive new solutions within the context of power-law $f(Q)$ gravity and the nonmetricity scalar-tensor theory. For the connection in the non-coincidence gauge, we present the point-like Lagrangian that describes the employed field equations. Furthermore, we construct two conservation laws, and for different values of these conserved quantities, we analytically solve the gravitational field equations. New solutions are obtained, we investigate their physical properties and their general relativistic limit. Finally, we discuss the algebraic properties for the derived spacetimes.

gr-qc↗

arXiv2024

Noether Symmetry Analysis for Generalized Brans-Dicke Cosmology

We present the complete solution to the classification problem regarding the variational symmetries of the generalized Brans-Dicke cosmological model in the presence of a second scalar field minimally coupled to gravity and the generalized Brans-Dicke scalar field theory. Through the symmetry analysis, we were able to specify the functional form of the field equations such that they become integrable. Additionally, new families of integrable cosmological models are presented.

gr-qc↗

arXiv2024

Lie Symmetries for the Shallow Water Magnetohydrodynamics Equations in a Rotating Reference Frame

We perform a detailed Lie symmetry analysis for the hyperbolic system of partial differential equations that describe the one-dimensional Shallow Water magnetohydrodynamics equations within a rotating reference frame. We consider a relaxing condition $\mathbf{\mathbf{\nabla }}\left( h\mathbf{B} \right) \neq 0$ for the one-dimensional problem, which has been used to overcome unphysical behaviors. The hyperbolic system of partial differential equations depends on two parameters: the constant gravitational potential $g$ and the Coriolis term $f_{0}$, related to the constant rotation of the reference frame. For four different cases, namely $g=0,~f_{0}=0$; $g\neq 0\,,~f_{0}=0$; $g=0$, $f_{0}\neq 0$; and $g\neq 0$, $f_{0}\neq 0$ the admitted Lie symmetries for the hyperbolic system form different Lie algebras. Specifically the admitted Lie algebras are the $L^{10}=\left\{ A_{3,3}\rtimes A_{2,1}\right\} \otimes _{s}A_{5,34}^{a}$; $% L^{8}=A_{2,1}\rtimes A_{6,22}$; $L^{7}=A_{3,5}\rtimes\left\{ A_{2,1}\rtimes A_{2,1}\right\} $; and $L^{6}=A_{3,5}\rtimes A_{3,3}~$respectively, where we use the Morozov-Mubarakzyanov-Patera classification scheme. For the general case where $f_{0}g\neq 0$, we derive all the invariants for the Adjoint action of the Lie algebra $L^{6}$ and its subalgebras, and we calculate all the elements of the one-dimensional optimal system. These elements are then considered to define similarity transformations and construct analytic solutions for the hyperbolic system.

math-ph↗

arXiv2024

Revise the Dark Matter-Phantom Scalar Field Interaction

The cosmological history and evolution are examined for gravitational models with interaction in the dark sector of the universe. In particular, we consider the dark energy to be described by a phantom scalar field and the dark matter $ρ_{m}$ as a pressureless ideal gas. We introduce the interacting function $Q=β\left( t\right) ρ_{m}$, where the function $% β\left( t\right) $ is considered to be proportional to $\dotϕ, \dotϕ^{2}H^{-1},~H$, or a constant parameter with dimensions of $\left[H_{0}\right] $. For the four interacting models, we study in details the phase space by calculating the stationary points. The latter are applied to reconstruct the cosmological evolution. Compactified variables are essential to understand the complete picture of the phase space and to conclude about the cosmological viability of these interacting models. The detailed analysis is performed for the exponential potential $V\left( ϕ\right) =V_{0}e^{λϕ}$. The effects of other scalar field potential functions on the cosmological dynamics are examined.

gr-qc↗

arXiv2024

Linearization of Newton's second law

The geometric linearization of nonlinear differential equation is a robust method for the construction of analytic solutions. The method is related to the existence of Lie symmetries which can be used to determine point transformations such that to write the given differential equation in a linear form. In this study we employ another geometric approach and we utilize the Eisenhart lift to geometric linearize the Newtonian system describing the motion of a particle in a line under the application of an autonomous force. Our findings reveal that for the oscillator, the Ermakov potential with or without the oscillator term, and the Morse potential, Newton's second law can be globally expressed in the form of that of a free particle. This study open new directions for the geometric linearization of differential equations via equivalent dynamical systems.

math-ph↗

arXiv2024

Generalized Scale factor Duality Symmetry in Symmetric Teleparallel Scalar-tensor FLRW Cosmology

We review the Gasperini-Veneziano scale factor duality symmetry for the dilaton field in scalar-tensor theory and its extension in teleparallelism. Within the framework of symmetric teleparallel scalar-tensor theory, we consider a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker metric cosmology. For the three possible connections, we write the corresponding point-like Lagrangians for the gravitational field equations, and we construct discrete transformations which generalize the Gasperini-Veneziano scale factor duality symmetry. The discrete transformations depend on the parameter which defines the coupling between the scalar field and the nonmetricity scalar. The Gasperini-Veneziano duality symmetry is recovered for a specific limit of this free parameter. Furthermore, we derive the conservation laws for the classical field equations for these models, and we present the origin of the discrete transformations. Finally, we discuss the integrability properties of the model, and exact solutions are determined.

gr-qc↗

arXiv2024

Compartmentalization and Coexistence in the Dark Sector of the Universe

We revise the cosmological interaction between dark energy and dark matter. More precisely, we focus on models that support compartmentalization or co-existence in the dark sector of the universe. Within the framework of a homogeneous and isotropic, spatially flat Friedmann--Lemaître--Robertson--Walker geometry, we analyse the asymptotic behaviour of the physical parameters for two interacting models, where dark energy and dark matter have constant equations of state parameters, in the presence of dark radiation, when dark energy is described by a quintessence scalar field. For each model, we determine the asymptotic solutions and attempt to understand how the interaction affects the cosmological evolution and history.

gr-qc↗

arXiv2024

The Equivalence Principle is NOT a Noether Symmetry

The connection between the Equivalence Principle and Noether's theorem was discussed in S. Capozziello and C. Ferrara, Int. J. Geom. Meth. Mod. Phys. 21, 2440014 (2024). However, it is known that the Noether symmetry condition is independent of the equations of motions as follows from Hamilton's Principle. In this paper, we critically examine the analysis presented in the aforementioned work, highlighting its flaws, and provide a detailed demonstration that there is no connection between Noether's theorem and the Equivalence Principle. Furthermore, we offer various insights on symmetry analysis to prevent the perpetuation of inaccuracies regarding Noether's work.

gr-qc↗

arXiv2024

The Common Solution Space of General Relativity

We review the solution space for the field equations of Einstein's General Relativity for various static, spherically symmetric spacetimes. We consider the vacuum case, represented by the Schwarzschild black hole; the de Sitter-Schwarzschild geometry, which includes a cosmological constant; the Reissner-Nordström geometry, which accounts for the presence of charge. Additionally we consider the homogenenous and anisotropic locally rotational Bianchi II spacetime in the vacuum. Our analysis reveals that the field equations for these scenarios share a common three-dimensional group of point transformations, with the generators being the elements of the $D\otimes_{s}T_{2}$ Lie algebra, known as the semidirect product of dilations and translations in the plane. Due to this algebraic property the field equations for the aforementioned gravitational models can be expressed in the equivalent form of the null geodesic equations for conformally flat geometries. Consequently, the solution space for the field equations is common, and it is the solution space for the free particle in a flat space. This appoach open new directions on the construction of analytic solutions in gravitational physics and cosmology.

gr-qc↗

arXiv2024

Semi-Classical limit and quantum corrections in noncoincidence power-law $f(Q)$-Cosmology

Within the framework of symmetric teleparallel $f\left( Q\right) $-gravity for a connection defined in the non-coincidence gauge we derive the Wheeler-DeWitt equation of quantum cosmology. Because the gravitational field equation in $f\left( Q\right) $-gravity admits a minisuperspace description the Wheeler-DeWitt equation is a single inhomogeneous partial differential equations. We assume the power-law $f\left( Q\right) =f_{0}Q^μ$ model and with the application of linear quantum observables we calculate the wavefunction of the universe. Finally, we investigate the effects of the quantum correction terms in the semi-classical limit.

gr-qc↗

arXiv2024

Geometric Linearization for Constraint Hamiltonian Systems

This study investigates the geometric linearization of constraint Hamiltonian systems using the Jacobi metric and the Eisenhart lift. We establish a connection between linearization and maximally symmetric spacetimes, focusing on the Noether symmetries admitted by the constraint Hamiltonian systems. Specifically, for systems derived from the singular Lagrangian $$ L\left( N,q^{k},\dot{q}^{k}\right) =\frac{1}{2N}g_{ij}\dot{q}^{i}\dot{q}^{j}-NV(q^{k}), $$ where $N$ and $q^{i}$ are dependent variables and $\dim g_{ij}=n$, the existence of $\frac{n\left( n+1\right) }{2}$ Noether symmetries is shown to be equivalent to the linearization of the equations of motion. The application of these results is demonstrated through various examples of special interest. This approach opens new directions in the study of differential equation linearization.

math-ph↗

arXiv2024

Dynamics of a higher-dimension Einstein-Scalar-Gauss-Bonnet cosmology

We study the dynamics of the field equations in a five-dimensional spatially flat Friedmann-Lemaître-Robertson-Walker metric in the context of a Gauss-Bonnet-Scalar field theory where the quintessence scalar field is coupled to the Gauss-Bonnet scalar. Contrary to the four-dimensional Gauss-Bonnet theory, where the Gauss-Bonnet term does not contribute to the field equations, in this five-dimensional Einstein-Scalar-Gauss-Bonnet model, the Gauss-Bonnet term contributes to the field equations even when the coupling function is a constant. Additionally, we consider a more general coupling described by a power-law function. For the scalar field potential, we consider the exponential function. For each choice of the coupling function, we define a set of dimensionless variables and write the field equations into a system of ordinary differential equations. We perform a detailed analysis of the dynamics for both systems and classify the stability of the equilibrium points. We determine the presence of scaling and super-collapsing solutions using the cosmological deceleration parameter. This means that our models can explain the Universe's early and late-time acceleration phases. Consequently, this model can be used to study inflation or as a dark energy candidate.

gr-qc↗

arXiv2024

Dipole Cosmology in $f(Q)$-gravity

Symmetric teleparallel $f(Q)$-gravity allows for the presence of a perfect fluid with a tilted velocity in the Kantowski-Sachs geometry. In this dipole model, we consider an ideal gas and we investigate the evolution of the physical parameters. The tilt parameter is constrained by the nonlinear function $f(Q)$ through the non-diagonal equations of the field equations. We find that the dynamics always reduce to the vacuum solutions of STEGR. This includes the Kasner universe, when no cosmological term is introduced by the $f(Q)$ function, and the isotropic de Sitter universe, where $f\left( Q\right) $ plays the role of the cosmological constant. In the extreme tilt limit, the universe is consistently anisotropic and accelerated. However, the final solution matches that of STEGR.

gr-qc↗

arXiv2024

Chameleon Mechanism in Scalar Nonmetricity Cosmology

We investigate the dynamics and the phase-space evolution for the scalar nonmetricity cosmology with a Chameleon mechanism. In particular, we consider a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker geometry and within the framework of scalar nonmetricity theory, we consider a generalization of the Brans-Dicke theory in nonmetricity gravity. Introducing a pressureless gas as the matter source, we also incorporate a coupling function responsible for the interaction. Our findings reveal that the choice of connection in nonmetricity gravity significantly impacts the interaction between the scalar field and the matter source. For one particular connection, we discover the absence of asymptotic solutions with a nontrivial interacting component. More precisely, in this scenario, the matter source does not directly interact with the scalar field; however, there is an interaction with the dynamical degrees of freedom provided by the connection.

gr-qc↗

arXiv2024

Bianchi I spacetimes in $f\left(Q\right)$-gravity

The Kasner spacetimes are exact solutions that are self-similar and of significant interest because they can describe the dynamic evolution of kinematic variables near the singularity of the Mixmaster universe. The chaotic behavior of the Mixmaster universe is related to the Kasner relations. This study investigates Kasner and Kasner-like solutions in symmetric teleparallel $f\left( Q\right) $-gravity. We consider three families of connections for the spatially flat Friedmann-Lema\^ıtre-Robertson-Walker. We found that Kasner-like solutions are present in the theory when the nonmetricity scalar $Q$ vanishes. Kasner-like relations are introduced only for the field equations of the connection defined in the coincidence gauge. Finally, we perform a detailed phase-space analysis to understand the dynamics of $f\left( Q\right) $-gravity in the evolution of anisotropies and the effects of different connections on this evolution.

gr-qc↗