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Contracting Universe (including bouncing models) solution generally depends on the initial conditions and hence possesses an extreme fine-tuning problem. In order to probe the stability of those solutions, in this work, we consider the…
Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. We show the fact that the linear-order metric perturbation is decomposed into gauge-invariant and gauge-variant…
This paper presents a systematic treatment of the linear theory of scalar gravitational perturbations in the synchronous gauge and the conformal Newtonian (or longitudinal) gauge. It differs from others in the literature in that we give, in…
We show that the linear dynamics of cosmological perturbations can be described by coupled wave equations, allowing their efficient numerical and, in certain limits, analytical integration directly in position space. The linear evolution of…
We present a scenario in which a scalar field dark energy is coupled to the trace of the energy momentum tensor of the baryonic matter fields. In the slow-roll regime, this interaction could give rise to the cosmological features of dark…
We briefly recall the problem of defining conserved quantities such as energy in general relativity, and the solution by introducing a symmetric background. We apply the general formalism to perturbed Robertson-Walker spacetimes with de…
We study in detail the phase space of a Friedmann-Robertson-Walker Universe filled with various cosmological fluids which may or may not interact. We use various expressions for the equation of state, and we analyze the physical…
In the context of f(R) theories of gravity, we study the cosmological evolution of scalar perturbations by using a completely general procedure. We find that the exact fourth-order differential equation for the matter density perturbations…
Whereas the nature of dark components in the Universe remains unknown, alternative models of gravity have been developed to offer a geometric explanation to the origin of such components. In this work we use the Minimal Geometric…
We consider solutions to nonlinear hyperbolic systems of balance laws with stiff relaxation and formally derive a parabolic-type effective system describing the late-time asymptotics of these solutions. We show that many examples from…
A generalised phase-space kinetic Boltzmann equation for highly non-equilibrium charged particle transport via localised and delocalised states is used to develop continuity, momentum and energy balance equations, accounting explicitly for…
A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which…
A transparent linear magneto-dielectric material in free space that is illuminated by a finite quasimonochromatic field is a thermodynamically closed system, definitively, regardless of what field and material subsystems that one defines.…
We review the study of inhomogeneous perturbations about a homogeneous and isotropic background cosmology. We adopt a coordinate based approach, but give geometrical interpretations of metric perturbations in terms of the expansion, shear…
A complete classification of exact solutions of ghost-free, massive bigravity is derived which enables the dynamical decoupling of the background, and the foreground metrics. The general decoupling solution space of the two metrics is…
We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which…
A new class of exact solutions of Einstein's field equations with a perfect fluid source, variable gravitational coupling $G$ and cosmological term $\Lambda$ for FRW spacetime is obtained by considering variable deceleration parameter…
Evolution of scalar perturbations in a universe containing solid matter with positive pressure is studied. Solution for pure solid is found and matched with solution for ideal fluid, including the case when the pressure to energy density…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
The paper proposes a novel cosmological model based on a two-field scenario, where the two fields are independently coupled with a specific invariant, based on cubic contractions of the Riemann tensor. After obtaining the modified Friedmann…