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The cosmic web (the arrangement of matter in the universe), spider's webs, and origami tessellations are linked by their geometry (specifically, of sectional-Voronoi tessellations). This motivates origami and textile artistic…
Cosmography, the study and making of maps of the universe or cosmos, is a field where visual representation benefits from modern three-dimensional visualization techniques and media. At the extragalactic distance scales, visualization is…
A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed…
This paper is an extended and more detailed version of arXiv:0812.0533. We tackle the problem of constructing explicit examples of topological cocycles of Roberts' net cohomology, as defined abstractly by Brunetti and Ruzzi. We consider the…
We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship…
We consider a gravitational field in steady state galaxy models of two kinds. Some of them are axisymmetrical and others are triaxial. Equipotentials and potential law are given separately in accordance to Kutuzov and Ossipkov (1980). The…
We overview our recent studies of cosmological models with expansion and global rotation. Problems of the early rotating models are discussed, and the class of new viable cosmologies is described in detail. Particular attention is paid to…
While the interpretation of high-dimensional datasets has become a necessity in most industries, and is supported by continuous advances in data science and machine learning, the spatial visualization of higher-dimensional geometry has…
A generalized quintessence model is presented which corresponds to a richer vacuum structure that, besides a time-dependent, slowly varying scalar field, contains a varying cosmological term. From first principles we determine a number of…
I consider the formulation of hybrid cosmological models that consists of a classical gravitational field interacting with a quantized massive scalar field in the formalism of ensembles on configuration space. This is a viable approach that…
We present a useful method for the construction of cosmological models by solving the differential equations arising from calculating the kinematical invariants (shear, rotation, expansion and acceleration) of an observer field in proper…
The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.
Gravitational Lensing is an efficient tool to probe: the mass distribution of collapsed systems: galaxies and clusters; high redshift objects thanks to the gravitational amplification; and the geometry of the Universe. I will review here…
An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand the theorems is supplied, the…
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and…
This work reviews the basic theoretical aspects, the main observational evidences and the recent applications of gravitational lensing in the Universe. The article is aimed particularly at providing the readers who don't work on…
In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential…
Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so…
The current status of the theoretical and observational cosmology is reviewed.