Related papers: First-order formalism for scalar field in cosmolog…
We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by…
We derive non-relativistic equations of motion for the formation of cosmological structure in a Scalar Field Dark Matter (SFDM) model corresponding to a complex scalar field endowed with a quadratic scalar potential. Starting with the full…
We provide two new classes of moment models for linear kinetic equations in slab and three-dimensional geometry. They are based on classical finite elements and low-order discontinuous-Galerkin approximations on the unit sphere. We…
We derive a second-order realizability-preserving scheme for moment models for linear kinetic equations. We apply this scheme to the first-order continuous and discontinuous models in slab and three-dimensional geometry derived in a…
In many cases a scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject particularly on type I Bianchi space-time. In this paper, global existence to the coupled…
The problem of algebraic dependence of solutions to (non-linear) first order autonomous equations over an algebraically closed field of characteristic zero is given a `complete' answer, obtained independently of model theoretic results on…
A new type of fluid matter model in general relativity is introduced, in which the fluid particles are subject to velocity diffusion without friction. In order to compensate for the energy gained by the fluid particles due to diffusion, a…
We introduce the notion of the cosmic numbers of a cosmological model, and discuss how they can be used to naturally classify models according to their ability to solve some of the problems of the standard cosmological model.
We look for exact solutions in scalar field cosmology. To achieve this we use $f(R)$ modified gravity with a scalar field and do not specify the the form of the $f(R)$ function. In particular, we study Friedmann universe assuming that…
Multifield models, arising from multiple scalars interacting with gravity, provide a rich theoretical framework for addressing fundamental problems in modern cosmology. A key role in this regard is played by the so called rapid turn regime,…
We consider multiple scalar fields coupled to gravity, with special attention given to two-field theories. First, the conditions necessary for these theories to meet solar system tests are given. Next, we investigate the cosmological…
Scalar fields appear in many theories beyond the Standard Model of particle physics. In the early universe, they are exposed to extreme conditions, including high temperature and rapid cosmic expansion. Understanding their behavior in this…
We formulate the equations of motion of a free scalar field in the flat and $AdS$ space of an arbitrary dimension in the form of some "higher spin" covariant constancy conditions. Klein-Gordon equation is interpreted as a non-trivial…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
We discuss the issue of motivating the analysis of higher order gravity theories and their cosmologies and introduce a rule which states that these theories may be considered as a vehicle for testing whether certain properties may be of…
A novel, interesting class of scalar-tensor gravity theories is those with a limit on the field motion, where the scalar field either goes to a constant acceleration or stops accelerating and goes to a constant velocity. We combine these…
Several isotropic, homogeneous cosmological models containing a self-interacting minimally coupled scalar field, a perfect fluid source and cosmological constant are solved. New exact, asymptotically stable solutions with an inflationary…
Local and global phase-space descriptions and averaging methods are used to find qualitative features of solutions for the FLRW and the Bianchi I metrics in the context of scalar field cosmologies with arbitrary potentials and arbitrary…
We present a new class of oscillons in the (1+1)-dimensional signum-Gordon model. The oscillons periodically move to and fro in the space. They have finite total energy, finite size, and are strictly periodic in time. The corresponding…
The correspondence of single-field cosmological models based on Einstein gravity to modern observational data is considered. A method is proposed to determine possible types of dynamics based on extreme values of the scalar field. It is…