Related papers: Scalar Field Cosmology -- Geometry of Dynamics
We investigate the interaction between systolic geometry and positive scalar curvature through spinorial methods. Our main theorem establishes an upper bound for the two-dimensional stable systole on certain high-dimensional manifolds with…
An attractive method of obtaining an effective cosmological constant at the present epoch is through the potential energy of a scalar field. Considering models with a perfect fluid and a scalar field, we classify all potentials for which…
The asymptotic behaviour of two classes of scalar field cosmological models are studied using the theory of dynamical systems: general relativistic Bianchi models containing matter and a scalar field with an exponential potential and a…
We review the appearance of multiple scalar fields in linearized SFT based cosmological models with a single non-local scalar field. Some of these local fields are canonical real scalar fields and some are complex fields with unusual…
In this article, we investigate scalar field cosmology in the coincident $f(Q)$ gravity formalism. We calculate the motion equations of $f(Q)$ gravity under the flat Friedmann-Lema\^{i}tre-Robertson-Walker background in the presence of a…
In multi-scalar field cosmologies new dynamical degrees of freedom are introduced which can explain the observational phenomena. Unlike the usual scalar field theory where a single scalar field is considered, the multi-scalar field…
A mathematical model of the evolution of spherical perturbations in a cosmological ideal scalar-charged fluid with scalar Higgs interaction is constructed. A closed mathematical model of linear spherical perturbations in a cosmological…
We develop a fully coupled theoretical description of dislocation dynamics on deformable crystalline surfaces, using continuum modeling and the amplitude-phase-field crystal (APFC) framework extended to curved geometries. We derive a…
A study and numerical modeling of the cosmological evolution of a classical scalar field with the Higgs potential was carried out. Based on the formulated similarity properties of cosmological models, their main characteristics are studied…
In the present work we perform a phase-plane analysis of the complete dynamical system corresponding to a flat FRW cosmological models with a perfect fluid and a self-interacting scalar field and show that every positive and monotonous…
We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…
We study a cosmological setup consisting of a FRW metric as the background geometry with a massless scalar field in the framework of classical polymerization of a given dynamical system. To do this, we first introduce the polymeric…
The dynamics of cosmic scalar fields with flat potential is studied. Their contribution to the expansion rate of the universe is analyzed, and their behaviour in a simple model of phase transitions is discussed.
We study multidimensional cosmological models with a higher-dimensional product manifold, that consists of spherical and flat spaces, in the presence of a minimal free scalar field. Dynamical behaviour of the model is analyzed both in…
A space-filling curve (SFC) maps points in a multi-dimensional space to one-dimensional points by discretizing the multi-dimensional space into cells and imposing a linear order on the cells. This way, an SFC enables the indexing of…
We study evolution of cosmological models filled with the scalar field and barotropic matter. We consider the scalar field minimally and non-minimally coupled to gravity. We demonstrated the growth of degree of complexity of evolutional…
In scaled relational particle mechanics, only relative times, relative angles and relative separations are meaningful. It arose in the study of the absolute versus relative motion debate. It has then turned out to be a useful toy model of…
Phantom energy can be visualized as a scalar field with a (non-canonical) negative kinetic energy term. We use the dynamical system formalism to study the attractor behavior of a cosmological model containing a phantom scalar field $\phi$…
We look for cosmologies with a scalar field (dark energy without cosmological constant), which mimic the standard $\Lambda CDM$ cosmological model yielding exactly the same large-scale geometry described by the evolution of the Hubble…
Mathematical models describing the cosmological evolution of classical and phantom scalar fields with self-action are formulated and analyzed. Systems of dynamical equations in the plane, describing homogeneous cosmological models, have…