相关论文: Lectures on Mathematical Cosmology
The current cosmological model, known as the $\Lambda$-Cold Dark Matter model (or $\Lambda$CDM for short) is one of the most astonishing accomplishments of contemporary theoretical physics. It is a well-defined mathematical model which…
Cosmology can be viewed as geodesic motion in an appropriate metric on an `augmented' target space; here we obtain these geodesics from an effective relativistic particle action. As an application, we find some exact (flat and curved)…
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…
A cosmological version of the holographic principle is proposed. Various consequences are discussed including bounds on equation of state and the requirement that the universe be infinite.
This article gives an overview, aimed at theoretical particle physicists, of some recent developments in cosmology.
We review cosmological relativity, a new special theory of relativity that was recently developed for cosmology, and discuss in detail some of its aspects.
In this lecture notes I concentrate on the classic and widely applicable characterization of higher order statistics by joint moments, a.k.a. higher order correlation functions, and directly related statistics. I put special emphasis on…
These lectures cover the basics of inflationary models for the early universe, concentrating particularly on the generation of density fluctuations from scalar-field dynamics. The subsequent gravitational dynamics of these fluctuations in…
In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…
The purpose of this paper is to expound and clarify the mathematics and explanations commonly employed in certain notable areas of astronomy and astrophysics. The first section concentrates upon the mathematics employed to represent and…
We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically,…
The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of…
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…
This is an introduction to loop quantum cosmology (LQC) reviewing mini- and midisuperspace models as well as homogeneous and inhomogeneous effective dynamics.
This is a review article for The Review of Particle Physics 2022 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters near the end of 2021. Topics included are Parametrizing the Universe;…
I describe the features and general properties of bouncing models and the evolution of cosmological perturbations on such backgrounds. I will outline possible observational consequences of the existence of a bounce in the primordial…
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
Microwave background polarization, though presently undetected, is a fundamental prediction of any viable cosmological model. These lectures review the theoretical description of polarization, its physical interpretation, and potentially…
Some contemporary views of the universe assume information and computation to be key in understanding and explaining the basic structure underpinning physical reality. We introduce the Computable Universe exploring some of the basic…
The topology of the large-scale structure of the universe contains valuable information on the underlying cosmological parameters. While persistent homology can extract this topological information, the optimal method for parameter…