Related papers: Cosmology of Plane Geometry
An introduction to modern cosmology is given, focusing on theories for the origin of structure in the Universe. After a brief review of the theory of growth of cosmological perturbations and a summary of some important observational…
A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points.…
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…
We study the geometry, Hodge theory and derived category of cubic fourfolds containing several planes and their associated twisted K3 surfaces. We focus on the case of two planes intersecting along a line.
We explore taxicab conic sections from the perspective of slicing taxicab cones by planes, as opposed to the more well-studied approach from the perspective of distance formulations. After establishing a significant amount of structural…
This is a review of cosmological models prepared for the Pont d'Oye workshop on the origin of structure in the universe. The classes of models are discussed in turn, and then some of their uses are considered.
Subject of this article is the relationship between modern cosmology and fundamental physics, in particular general relativity as a theory of gravity on one side, together with its unique application in cosmology, and the formation of…
In this brief essay we consider the concept of beginning in cosmology. It can be applied to the Universe as a whole, as well as to various epochs in the cosmic history and major structures as we can see them today.
The light we observe from distant astrophysical objects including supernovae and quasars allows us to determine large distances in terms of a cosmological model. Despite the success of the standard cosmological model in fitting the data,…
In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and…
Recent years have seen dramatic progress in cosmology and particle astrophysics. So much so that anyone who dares to offer an overview would certainly risk him- or herself for being incomplete and biased at best, and even incorrect due to…
This lecture note is hopefully helpful to undergraduate and postgraduate students or beginning Ph.D students both in theoretical physics and in applied mathematics. Modern terminology in differential geometry has been discussed in the book…
This is a review article for The Review of Particle Physics 2014 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters at the beginning of 2014. Topics included are Parametrizing the Universe;…
Non Conventional treatments in modern cosmology, in both Steady State and Big Bang, are given. The motivation behind these treatments is to solve some of the problems of the conventional treatments in cosmology. For this aim, different…
We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…
In a recent paper (arXiv:1412.6000) a general mechanism for emergence of cosmological space-time geometry from a quantum gravity setting was devised and departure from standard dispersion relations for elementary particle were predicted. We…
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance…
An introductory lectures on cosmology at ITEP Winter School for students specializing in particle physics are presented. Many important subjects are not covered because of lack of time and space but hopefully the lectures may serve as a…
We survey some old and new results about acyclic (affine) complex surfaces, also called homology planes. We ask several questions and leave open directions for future research.