arXiv subjects
Publications and source records attributed to Andronikos Paliathanasis.
We explore the introduction of the cosmological constant via equivalent transformations in cosmology. We consider the Wheeler-DeWitt equation for the CDM universe and we construct the Hamilton-Jacobi action for the $Λ$CDM model. We discuss how this approach allows us to relate different physical systems, providing insights into the role of the cosmological constant in cosmology.
We investigate the asymptotic behavior of the cosmological field equations in Symmetric Teleparallel General Relativity, where a nonlinear function of the boundary term is introduced instead of the cosmological constant to describe the acceleration phase of the universe. Our analysis reveals constraints on the free parameters necessary for the existence of an attractor that accurately represents acceleration. However, we also identify asymptotic solutions depicting Big Rip and Big Crunch singularities. To avoid these solutions, we must impose constraints on the phase-space, requiring specific initial conditions.
Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases where the power law is observed accurately. Fractional calculus must reflect non-local, frequency- and history-dependent properties of power-law phenomena. This tool has various important applications, such as fractional mass conservation, electrochemical analysis, groundwater flow problems, and fractional spatiotemporal diffusion equations. It can also be used in cosmology to explain late-time cosmic acceleration without the need for dark energy. We review some models using fractional differential equations. We look at the Einstein--Hilbert action, which is based on a fractional derivative action, and add a scalar field, $ϕ$, to create a non-minimal interaction theory with the coupling, $ξR ϕ^2 $, between gravity and the scalar field, where $ξ$ is the interaction constant. By employing various mathematical approaches, we can offer precise schemes to find analytical and numerical approximations of the solutions. Moreover, we comprehensively study the modified cosmological equations and analyze the solution space using the theory of dynamical systems and asymptotic expansion methods. This enables us to provide a qualitative description of cosmologies with a scalar field based on fractional calculus formalism.
Inspired by the generalization of scalar field gravitational models with a minimum length we study the equivalent theory in modified theories of gravity. The quadratic Generalized Uncertainty Principle (GUP) gives rise to a deformed Heisenberg algebra in the application, resulting in the emergence of additional degrees of freedom described by higher-order derivatives. The new degrees of freedom can be attributed to the introduction of a new scalar field, trasforming the resulting theory into a two-scalar field theory. Thus, in order to describe all the degrees of freedom we investigate special forms of the sixth-order modify $f\left( R,\square R\right) -$theory of gravity, where the gravitational Lagrangian has similar properties~to~that of the GUP scalar field theory. Finally, the cosmological applications are discussed, and we show that the de Sitter universe can be recovered without introducing a cosmological constant.
We explore the phase-space of a multiscalar-torsion gravitational theory within a cosmological framework characterized by a spatially flat Friedmann-Lema\^ıtre-Robertson-Walker model. Our investigation focuses on teleparallelism and involves a gravitational model featuring two scalar fields, where one scalar field is coupled to the torsion scalar. We consider coupling in the two scalar fields' kinetic and potential components. We employ exponential functions for the scalar field potentials and analyze the field equations' equilibrium points to reconstruct the cosmological evolution. Remarkably, we discover many equilibrium points in this multiscalar field model, capable of describing various eras of cosmological evolution. Hence, this model can be used to describe the early and late time acceleration phases of the universe and as a unification model for the elements of the dark sector of the universe.
This study introduces a novel approach for solving the cosmological field equations within scalar field theory by employing the Eisenhart lift. The field equations are reformulated as a system of geodesic equations for the Eisenhart metric. In the case of an exponential potential, the Eisenhart metric is shown to be conformally flat. By applying basic geometric principles, a new set of dynamical variables is identified, allowing for the linearization of the field equations and the derivation of classical cosmological solutions. However, the quantization of the Eisenhart system reveals a distinct set of solutions for the wavefunction, particularly in the presence of symmetry breaking at the quantum level.
We investigate the impact of conformal transformations on the physical properties of solution trajectories in nonmetricity gravity. Specifically, we explore the phase-space and reconstruct the cosmological history of a spatially flat Friedmann-Lema\^ıtre-Robertson-Walker universe within scalar-nonmetricity theory in both the Jordan and Einstein frames. A detailed analysis is conducted for three different connections defined in both the coincident and non-coincident gauges. Our findings reveal the existence of a unique one-to-one correspondence for equilibrium points in the two frames. Furthermore, we demonstrate that solutions describing accelerated universes remain invariant under the transformation that relates these conformally equivalent theories.
We consider the Brans-Dicke theory in non-metricity gravity, which belongs to the family of symmetric teleparallel scalar-tensor theories. Our focus lies in exploring the implications of the conformal transformation, as we derive the conformal equivalent theory in the Einstein frame, distinct from the minimally coupled scalar field theory. The fundamental principle of the conformal transformation suggests the mathematical equivalence of the related theories. However, to thoroughly analyze the impact on physical variables, we investigate the spatially flat Friedmann--Lema\^ıtre--Robertson--Walker geometry, defining the connection in the non-coincidence gauge. We construct exact solutions for the cosmological model in one frame and compare the physical properties in the conformal related frame. Surprisingly, we find that the general physical properties of the exact solutions remain invariant under the conformal transformation. Finally, we construct, for the first time, an analytic solution for the symmetric teleparallel scalar-tensor cosmology.
We address the group classification problem for gravitational field equations within the context of brane-world cosmology, considering the presence of a bulk scalar field. Our investigation revolves around a five-dimensional spacetime, with the four-dimensional Friedmann--Lema\^ıtre--Robertson--Walker geometry embedded within it. Additionally, we assume that the scalar field exists in this five-dimensional geometry (bulk) and possesses a nonzero mass. The resulting field equations constitute a system of nonlinear partial differential equations. We apply the Lie symmetry condition to identify all functional forms of the scalar field potential, ensuring that the field equations remain invariant under one-parameter point transformations. Consequently, we find that only the exponential potential exhibits Lie symmetries. Finally, the Lie invariants are used to construct similarity transformations, which enable us to derive exact solutions for the system.
We consider the symmetric teleparallel $f\left( Q\right) $-gravity in Friedmann--Lema\^ıtre--Robertson--Walker cosmology with nonzero spatial curvature. For a nonlinear $f\left( Q\right) $ model there exist always the limit of General\ Relativity with or without the cosmological constant term. The de Sitter solution is always provided by the theory and for the specific models $f_{A}\left( Q\right) \simeq Q^{\fracα{α-1}}% ~,~f_{B}\left( Q\right) \simeq Q+f_{1}Q^{\fracα{α-1}}$ and $f_{C}\left( Q\right) \simeq Q+f_{1}Q\ln Q$ it was found to be the unique attractor. Consequently small deviations from STGR can solve the flatness problem and lead to a de Sitter expansion without introduce a cosmological constant term. This result is different from that given by the power-law theories for the other two scalar of the trinity of General Relativity. What makes the nonlinear symmetric teleparallel theory to stand out are the new degree of freedom provided by the connection defined in the non-coincidence frame which describes the nonzero spatial curvature.
We investigate the geometrodynamical effects of introducing the boundary term in symmetric teleparallel gravity. Specifically, we consider a homogeneous and isotropic universe in $f\left( Q, B \right) $, where $Q$ is the non-metricity scalar, and $B$ is the boundary term that relates the non-metricity and Ricci scalars. For the connection in the coincidence gauge, we find that the field equations are of fourth-order, and the fluid components introduced by the boundary are attributed to a scalar field. In the coincidence gauge, the cosmological field equations are equivalent to those of teleparallelism with a boundary term. Nevertheless, for the connection defined in the non-coincidence gauge, the geometrodynamical fluid consists of three scalar fields. We focus on the special case of $f\left( Q, B \right) = Q + F\left( B \right) $ theory, and we determine a new analytic cosmological solution that can explain the late-time acceleration of the universe and provide a geometric mechanism for the unification of dark energy with dark matter.
For a spatially Friedmann-Lema\^ıtre-Robertson-Walker cosmology, we propose a multi-scalar field gravitational model. Specifically, we consider a two-scalar field cosmological model in which the kinetic components of the scalar fields establish a two-dimensional sphere of Lorentzian signature. For our Chiral-Quintom model we choose a mixed potential term $V( ϕ,ψ) =V_{0}e^{λϕ}+U_{0}e^{κϕ}ψ^{\frac{1}σ}$ and we investigate the asymptotic limits of the cosmological parameters. This model for $U_{0}=0$, provides a generalization of the hyperbolic inflation where the equation of the state parameter can cross the phantom divide line. When $U_{0}\neq0$ we observe that this cosmological model exhibits asymptotic solutions that encompass accelerated universes, big rip singularities, and dust-like solutions. Hence, this multi-scalar field model it can be regarded as as a dark energy unify model which describes a variety of asymptotic cosmological scenarios.
We comprehensively analyze the dynamics for the gravitational field equations for the Chiral-Quintom theory in a Friedman-Lemaître-Robertson-Walker cosmology with an additional matter source. We consider a new set of dimensionless variables and write the field equations in the equivalent form of an algebraic-differential system. Specifically, we consider two families of quintom models where the two scalar fields interact in the kinetic sector. We mathematically focus on the dynamical effect of spatial curvature. Physically, we find two periods of inflation related to the Universe's early and late-time acceleration phases.
We apply the Noether symmetries to constrain the unknown functions of chameleon gravity in the cosmological scenario of a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker space-time with an ideal gas. For this gravitational model the field equations admit a point-like Lagrangian with as unknown functions the scalar field potential and the coupling function which is responsible for the chameleon mechanism. Noether's first theorem provides us with four sets of closed-form functional forms for which variational symmetries exist. We construct the corresponding conservation laws and we use them in order to determine new analytic solutions in chameleon gravity. From the analysis of the physical properties of the new solution it follows that in the late universe they can reproduce the $Λ$CDM model without having to assume the presence of a pressureless fluid in the cosmological fluid.
We present a detailed analysis of the phase-space for the field equations in scalar field cosmology with a chameleon cosmology in a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker spacetime. For the matter source we assume that it is an ideal gas with a constant equation of state parameter, while for the scalar field potential and the coupling function of the chameleon mechanism we consider four different sets which provide four different models. We consider the $H$-normalization approach and we write the field equations with the help of dimensionless variables. The asymptotic solutions are determined from where we find that the theory can describe the main eras of cosmological history and evolution. Future attractors which describe acceleration exist, however we found past acceleration solutions related to the inflationary era, as also the radiation epoch and the matter dominated eras are provided by the dynamics. We conclude that the Chameleon dark energy model can be used as a unified model for the elements which contribute to the dark sector of the universe.
We present a complete algebraic classification of the Lie symmetries for generalized Zoomeron equations. For the generalized 1+1 and 2+1 Zoomeron equations we solve the Lie symmetry conditions in order to constrain the free functions of the equations. We find that the differential equations of our consideration admit the same number of Lie symmetries with the non-generalized equations. The admitted Lie symmetries form the Lie algebras $2A_{1}$, $A_{3,3}$ $\ $for the 1+1 generalized Zoomeron equation, and the $% A_{4,5}^{ab}\,$, $3A_{1}\otimes _{s}2A_{1}$ in the case of the 2+1 generalized Zoomeron equation. The one-dimensional optimal system is constructed for the two equations and similarity solutions are derived.\ The similarity transformation lead to the derivation of kink solutions. Indeed, the similarity exact solutions determined in this work are asymptotic solutions near to the singular behaviour of the kink behaviour.
We study the evolution of the physical variables in $f\left( Q\right) $-gravity for two families of symmetric and flat connections in a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker geometry where the equation of motion for the nonmetricity scalar is not trivially identity. From the analysis of dynamics we found that the de Sitter universe is always an attractor while the cosmological models admit scaling solutions which can describe the early acceleration phase of our universe or the matter and the radiation epochs.
We study the dynamics of the field equations in a four-dimensional isotropic and homogeneous spatially flat Friedmann--Lema\^ıtre--Robertson--Walker geometry in the context of Einstein-Gauss-Bonnet theory with a matter source and a scalar field coupled to the Gauss-Bonnet scalar. In this theory, the Gauss-Bonnet term contributes to the field equations. The mass of the scalar field depends on the potential function and the Gauss-Bonnet term. For the scalar field potential, we consider the exponential function and the coupling function between the scalar field and the Gauss-Bonnet scalar is considered to be the linear function. Moreover, the scalar field can have a phantom behaviour. We consider a set of dimensionless variables and write the field equations into a system or algebraic-differential equations. For the latter, we investigate the equilibrium points and their stability properties. In order to perform a global analysis of the asymptotic dynamics, we use compactified variables. This gravitational theory can explain the Universe's recent and past acceleration phases. Therefore, it can be used as a toy model for studying inflation or as a dark energy candidate.