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We study the weak solvability of a nonlinearly coupled system of parabolic and pseudo-parabolic equations describing the interplay between mechanics, chemical reactions, diffusion and flow in a mixture theory framework. Our approach relies…
This work discusses scalar-tensor theories of gravity, with a focus on the Brans-Dicke subclass, and one that also takes note of the latter's equivalence with $f(R)$ gravitation theories. A 1+3 covariant formalism is used in this case to…
In this paper, we analyze a two coupled fluids model by investigating several solutions for accelerated universe in flat FRW space-time. One of the fluids can be identified with the matter and the model possesses the standard matter…
In our companion paper we identified a complete set of manifestly gauge-invariant observables for general relativity. This was possible by coupling the system of gravity and matter to pressureless dust which plays the role of a dynamically…
A manifestly covariant equation is derived to describe the second order perturbations in topological defects and membranes on arbitrary curved background spacetimes. This, on one hand, generalizes work on macroscopic strings in Minkowski…
Hyperbolic systems under nonconservative form arise in numerous applications modeling physical processes, for example from the relaxation of more general equations (e.g. with dissipative terms). This paper reviews an existing class of…
We construct an approximate solution to the cosmological perturbation theory around Einstein-de Sitter background up to the fourth-order perturbations. This could be done with the help of the specific symmetry condition imposed on the…
We study cosmological perturbations for a ghost free massive gravity theory formulated with a dynamical extra metric that is needed to massive deform GR. In this formulation FRW background solutions fall in two branches. In the dynamics of…
We present a covariant and gauge invariant formalism suited to the study of second-order effects associated with higher order tensor perturbations. The analytical method we have developed enables us to characterize pure second-order tensor…
Cosmological perturbations are considered in $f(T)$ and in scalar-torsion $f(\varphi)T$ teleparallel models of gravity. Full sets of linear perturbation equations are accurately derived and analysed at the relevant limits. Interesting…
A model for the Universe is proposed whose constituents are: (a) a dark energy field modeled by a fermionic field non-minimally coupled with the gravitational field, (b) a matter field which consists of pressureless baryonic and dark matter…
We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive…
We consider the evolution of perturbed cosmological spacetime with multiple fluids and fields in Einstein gravity. Equations are presented in gauge-ready forms, and are presented in various forms using the curvature (\Phi or \phi_\chi) and…
We determine the Hubble expansion and the general cosmic perturbations equations for a general system consisting of self-conserved matter and self-conserved dark energy (DE). While at the background level the two components are…
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…
An alternative cosmological model is presented, which avoids the requirement of dark energy and dark matter. Based on the proposition that energy conservation should be valid not only locally but also globally, the energy tensor of general…
We discuss scalar-tensor realizations of the Anamorphic cosmological scenario recently proposed by Ijjas and Steinhardt. Through an analysis of the dynamics of cosmological perturbations we obtain constraints on the parameters of the model.…
Teleparallel gravity offers a new avenue in which to construct gravitational models beyond general relativity. While teleparallel gravity can be framed in a way to be dynamically equivalent to general relativity, its modifications are…
We obtain the perturbed components of affine connection and Ricci tensor using algebraic computation. Naturally, the perturbed Einstein field equations for the vacuum can be written. The method can be used to obtain perturbed equations of…
We review and extend a novel approach that we introduced recently, to describe general dark energy or scalar-tensor models. Our approach relies on an ADM formulation based on the hypersurfaces where the underlying scalar field is uniform.…