Related papers: Cosmology of Plane Geometry
We have constructed a nonlinear multi-graviton theory. An application of this theory to cosmology is discussed. We found that scale factors in a solution for this theory repeat acceleration and deceleration.
In this chapter it is shown how the introduction of a fundamental constant of nature with dimensions of acceleration into the theory of gravity makes it possible to extend gravity in a very consistent manner.
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
While purely philosophical in the early times, and still very speculative at the beginning of the twentieth century, Cosmology has gradually entered into the realm of experimental science over the past eighty years. It has raised some…
An innovative approach to map the large-scale structure in the Universe sidesteps the conventional need to observe millions of galaxies individually, and holds promise for both astrophysical and cosmological studies.
Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…
The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…
The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples…
Cosmological observations are beginning to reach a level of precision that allow us to test some of the most fundamental assumptions in our working model of the Universe. One such an assumption is that gravity is governed by the General…
This is a review article for The Review of Particle Physics 2020 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters at the end of 2019. Topics included are Parametrizing the Universe;…
The geometric foundations of General Relativity are revisited, with particular attention to its gauge invariance, as a key to understanding the true nature of spacetime. Beyond the common image of spacetime as a deformable 'fabric' filling…
This collection of perspective pieces captures recent advancements and reflections from a dynamic research community dedicated to bridging quantum gravity, hydrodynamics, and emergent cosmology. It explores four key research areas: (a) the…
It is proposed that the mathematical formalism that is most appropriate for the study of spatially non-integrable cosmological models is the transverse geometry of a one-dimensional foliation (congruence) defined by a physical observer. By…
In recent years, by theory and observation cosmology has advanced substantially. Parameters of the concordance or $\Lambda$CDM cosmological model are given with unprecedented precision ("precision cosmology"). On the other side, 95% of the…
This is a survey article on the recent development of "stringy geometry and topology of orbifolds", a new subject of mathematics motivated by orbifold string theory.
We find a geometrical method of analysing the singularities of a plane nodal curve. The main results will be used in a forthcoming paper on geometric Plucker formulas for such curves. Plane nodal curves, that is plane curves having at most…
A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.
This is a review article for The Review of Particle Physics 2006 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters as at May 2006. Topics included are Parametrizing the Universe; Extensions…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
We present a non-physical interpretation of the Cosmological Constant based on a particular algebraic analysis. This also introduces some novel algebraic structures, such as ``unital norms", ``uncurling metrics", and ``partial wedge…