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We study the phase space dynamics of cosmological models in the theoretical formulations of non-minimal metric-torsion couplings with a scalar field, and investigate in particular the critical points which yield stable solutions exhibiting…
A detailed comparative qualitative analysis and numerical simulation of evolution of the cosmological models based on the doublet of classical and phantom scalar fields with self-action. The 2-dimensional and 3-dimensional projections of…
It is useful to study the space of all cosmological models from a dynamical systems perspective, that is, by formulating the Einstein field equations as a dynamical system using appropriately normalized variables. We will discuss various…
We consider scalar perturbations of energy-density for a class of cosmological models where an early phase of accelerated expansion evolves, without any fine-tuning for graceful exit, towards the standard Friedman eras of observed universe.…
We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean ${\Bbb{R}}^3$ and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces…
An analytic approach to phenomenological models inspired by cubic string field theory is introduced and applied to some examples. We study a class of actions for a minimally coupled, homogeneous scalar field whose energy density contains…
A model of topological field theory is presented in which the vacuum coupling constants are topological invariants of the four-dimensional spacetime. Thus the coupling constants are theoretically computable, and they indicate the…
We study the phase space of spatially homogeneous and isotropic cosmology in general scalar-tensor theories. A reduction to a two-dimensional phase space is performed when possible-in these situations the phase space is usually a…
In this work, a cosmological model is considered having two scalar fields minimally coupled to gravity with a mixed kinetic term. The model is characterized by the coupling function and the potential function which are assumed to depend on…
Locally inertial coordinates are constructed by carrying Riemann normal coordinates on a codimension two spacelike surface along the geodesics normal to it. Since the normal tangents are labelled by components with respect to a null basis,…
In this paper, we introduce discrete approximate circle bundles, a class of objects designed to serve as the data science analog of circle bundles from algebraic topology. We show that, under appropriate conditions, one can meaningfully and…
We construct integrable chiral cosmological models with two scalar fields and potentials represented in terms of hyperbolic functions. Using the conformal transformation of the metric and the corresponding models with induced gravity terms,…
In this work we study different aspect of self-interacting 2-form fields with special emphasis in their cosmological applications. We provide the explicit construction of how massless 2-forms are compatible with the cosmological principle…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
We propose a class of two-field cosmological models derived from gravity coupled to non-linear sigma models whose target space is a non-compact and geometrically-finite hyperbolic surface, which provide a wide generalization of so-called…
We compute the curvature tensor of the tangent bundle of a Riemannian manifold endowed with a natural metric and we get some relationships between the geometry of the base manifold and the geometry of the tangent bundle.
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
We develop the theory of arrangements of spheres. Consider a finite collection of codimension-$1$ subspheres in a positive-dimensional sphere. There are two posets associated with this collection: the poset of faces and the poset of…
The subject of the paper is the geometry and topology of cosmological spacetimes and vector bundles thereon, which are used to model physical fields propagating in the universe. Global hyperbolicity and factorization properties of the…
We consider the Noether Symmetry Approach for a cosmological model derived from a tachyon scalar field $T$ with a Dirac-Born-Infeld Lagrangian and a potential $V(T)$. Furthermore, we assume a coupled canonical scalar field $\phi$ with an…