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Light scalar fields very naturally appear in modern cosmological models, affecting such parameters of Standard Model as electromagnetic fine structure constant $\alpha$, dimensionless ratios of electron or quark mass to the QCD scale,…
We study the first order infared behavior of tame hyperbolizable two-field cosmological models, defined as those classical two-field models whose scalar manifold is a connected, oriented and topologically finite hyperbolizable Riemann…
By directly probing the initial conditions of our universe, cosmological surveys offer us a unique observational handle on quantum field theory in curved spacetime with dynamical gravity and might even allow us to glean information about a…
For a manifold embedded in an inner product space, we express geometric quantities such as {\it Hamilton vector fields, affine and Levi-Civita connections, curvature} in global coordinates. Instead of coordinate indices, the global formulas…
We consider here a spherically symmetric but inhomogeneous universe filled with a massless scalar field. The model obeys two constraints. The first one is that the gradient of the scalar field is timelike everywhere. The second constraint…
The aim of this paper is two-fold. First, we define symplectic maps between Hitchin systems related to holomorphic bundles of different degrees. We call these maps the Symplectic Hecke Correspondence (SHC) of the corresponding Higgs…
In two previous papers, we constructed two modified Hamiltonian formalisms to make maps among manifolds explicit. In this paper, the two modified formalisms were adapted to manifolds with local coordinates given by scalar fields, as in a…
Finding constrained saddle points on Riemannian manifolds is significant for analyzing energy landscapes arising in physics and chemistry. Existing works have been limited to special manifolds that admit global regular level-set…
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 detailed comparative qualitative analysis and numerical simulation of evolution of the cosmological models based on classical and phantom scalar fields with self-action was performed. The phase portraits of the dynamic systems of…
The quantum theory of near horizon regions of spacetimes with classical spatially flat, homogeneous and isotropic Friedman-Robertson-Walker geometry can be approximately described by a two dimensional conformal field theory. The central…
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic…
On the basis of the relativistic kinetic theory the mathematical model of cosmological plasmas with an attraction of the like charged scalar particles is formulated. It is shown, that cosmological the model, based on a classical scalar…
The structure formation in the local Universe is considered within the weak-field modification of General Relativity involving the cosmological constant. This approach enables to describe the dynamics of groups and clusters of galaxies, to…
We develop a hybrid GNN-CNN architecture for the reconstruction of 3-dimensional continuous cosmological matter fields from discrete point clouds, provided by observed galaxy catalogs. Using the CAMELS hydrodynamical cosmological…
The standard description of cosmological observables is incomplete, because it does not take into account the correct angular parametrization of the sky, i.e. the one determined by the observer frame. The corresponding corrections must be…
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…
Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates…
Given a field of Hilbert spaces there are two ways to endow it with a smooth structure: the standard and geometrical notion of Hilbert (or Hermitian) bundle and the analytical notion of smooth field of Hilbert spaces. We study the…
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…