Related papers: Natural observables and dynamical approximations i…
The paper deals with a dynamical system analysis related to phantom cosmological model . Here gravity is coupled to phantom scalar field having scalar coupling function and a potential. The field equations are reduced to an autonomous…
We discuss the study of topological characteristics of random fields that are used for numerical simulation of oil and gas reservoirs and numerical algorithms (see arXiv:1302.3669), for computing such characteristics, for which we…
We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…
We review the most recent progress in our understanding of quantum mechanical observables in cosmology in the perturbative regime. It relies on an approach that considers them directly as functions of the data at the space-like boundary at…
The current status of the theoretical and observational cosmology is reviewed.
Anthropic solutions to the cosmological constant problem require seemingly unnatural scalar field potentials with a very small slope or domain walls (branes) with a very small coupling to a four-form field. Here we introduce a class of…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
We place the theory of metric Diophantine approximation on manifolds into a broader context of studying Diophantine properties of points generic with respect to certain measures on $\Bbb R^n$. The correspondence between multidimensional…
We consider a superconformal quantum mechanical system which has been chosen on the basis of a local BRST topological invariance. We suggest that it truly leads to topological observables which we compute. The absences of a ground state and…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of…
Modified gravity theories can be used for the description of homogeneous and isotropic cosmological models through the corresponding field equations. These can be cast into systems of autonomous differential equations because of their sole…
Cosmological observables are used to construct cosmological models. Since cosmological observations are limited to the light cone, a fixed number of observables (even measured to arbitrary accuracy) may not uniquely determine a cosmological…
We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle…
We derive a new \emph{regular} dynamical system on a 3-dimensional \emph{compact} state space describing linear scalar perturbations of spatially flat Robertson-Walker geometries for relativistic models with a minimally coupled scalar field…
A numerical coincidence relating the values of the cosmological, gravitational and electromagnetic fine structure constants is presented and discussed in relation to the apparent anthropic fine-tuning of these three fundamental constants of…
A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…
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.
In this paper we study the monomial dynamical systems of dimension one over finite fields from the viewpoints of arithmetic and graph theory. We give formulas for the number of periodic points with period r and cycles with length r. Then we…