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We investigate the dynamics of Einstein equations in the vicinity of the two recently described types of singularity of anisotropic and homogeneous cosmological models described by the action $$ S=\int d^4x \sqrt{-g}{F(\phi)R -…
We provide a detailed study of the properties of a few interacting spin $1/2$ fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical…
We study the cosmological evolution of the field equations in the context of Einstein-Aether cosmology by including a scalar field in a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. Our analysis is separated into two…
The asymptotic properties of conformally static metrics in Einstein-aether theory with a perfect fluid source and a scalar field are analyzed. In case of perfect fluid, some relativistic solutions are recovered such as: Minkowski spacetime,…
We investigate the cosmological dynamics of interacting dark energy models in which the interaction function is a nonlinear in terms of the energy densities. Considering explicitly the interaction between a pressureless dark matter and a…
We study an inflation mechanism based on attractor properties in cosmological evolutions of a spatially flat Friedmann-Robertson-Walker spacetime based on the Einstein-scalar field theory. We find a new way to get the Hamilton-Jacobi…
Self-consistent solutions to interacting spinor and scalar field equations in General Relativity are studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions…
A self-consistent system of interacting spinor and scalar fields is considered within the scope of Bianchi type VI cosmological model filled with a perfect fluid. The contribution of the cosmological constant ($\Lambda$-term) is taken into…
We provide a detailed description for power--law scaling Friedmann-Robertson-Walker cosmological scenarios dominated by two interacting perfect fluid components during the expansion. As a consequence of the mutual interaction between the…
We examine in the context of general relativity the dynamics of a spatially flat Robertson-Walker universe filled with a classical minimally coupled scalar field \phi of exponential potential ~ e^{-\mu\phi} plus pressureless baryonic…
We consider a massless minimally coupled self interacting quantum scalar field coupled to fermion via the Yukawa interaction, in the inflationary de Sitter background. The fermion is also taken to be massless and the scalar potential is…
The effective equation of motion is derived for a scalar field interacting with other fields in a Friedman-Robertson-Walker background space-time. The dissipative behavior reflected in this effective evolution equation is studied both in…
The time evolution of O(N) symmetric lambda Phi^4 scalar field theory is studied in the large N limit. In this limit the <Phi> mean field and two-point correlation function <Phi Phi> evolve together as a self-consistent closed Hamiltonian…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
We investigate the cosmological dynamics of non-minimally coupled scalar field system described by $F(\phi)R$ coupling with $F(\phi)=(1-\xi\phi^N)R$($N\ge2$) and the field potential, $V(\phi)=V_0\phi^n$. We use a generic set of dynamical…
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
We investigate relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space,…
We review the attractor properties of the simplest chaotic model of inflation, in which a minimally coupled scalar field is endowed with a quadratic scalar potential. The equations of motion in a flat Friedmann-Robertson-Walker universe are…