Related papers: Current Trends in Mathematical Cosmology
For two decades the hot big-bang model as been referred to as the standard cosmology -- and for good reason. For just as long cosmologists have known that there are fundamental questions that are not answered by the standard cosmology and…
In this short review we study the state of the art of the great problems in cosmology and their interrelationships. The reconciliation of these problems passes undoubtedly through the idea of a quantum universe.
We refer to the classic definition of a singularity in Einstein's general relativity (based on geodesic incompletness) as well as to some other criteria to evaluate the nature of singularities in cosmology. We review what different…
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…
Two fundamental laws are needed for prediction in the universe: (1) a basic dynamical law and (2) a law for the cosmological initial condition. Quantum cosmology is the area of basic research concerned with the search for a theory of the…
The cosmological constant problem is one of the greatest challenges in contemporary physics, since it is deeply rooted in the problematic interplay between quantum fields and gravity. The aim of this work is to review the key conceptual…
We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized.
Sujets qui sont plus particulierement abordes dans ce cours: 1. Elements de cosmologie, l'Univers homogene Les principes cosmologiques et leurs verifications observationnelles Histoire thermique de l'Univers Inflation, motivations et…
Varying physical constant cosmologies were claimed to solve standard cosmological problems such as the horizon, the flatness and the $\Lambda$-problem. In this paper, we suggest yet another possible application of these theories: solving…
In this essay a critical review of present conceptual problems in current cosmology is provided from a more philosophical point of view. In essence, a digression on how could philosophy help cosmologists in what is strictly their…
The scientific status of physical cosmology has been the subject of philosophical debate ever since detailed mathematical models of the Universe emerged from Einstein's general theory of relativity. Such debates have revolved around whether…
The present talk summarizes the recently progressed state of a systematic re-evaluation of cosmological models that respect the presence of inhomogeneities. Emphasis is given to identifying the basic steps towards an effective (i.e.…
This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving…
One of the most enduring and unresolved challenges in modern theoretical and observational cosmology is the fine-tuning and coincidence problems associated with the cosmological constant. Rather than attempting to reconcile these issues…
The question of the nature of galaxy clustering and the possible homogeneity of galaxy distribution is one of the fundamental problem of cosmology. It is well established that galaxy structures are characterized, up to a certain scale, by…
In this letter we will revise the steps followed by A. Einstein when he first wrote on cosmology from the point of view of the general theory of relativity. We will argue that his insightful line of thought leading to the introduction of…
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…
We have a well-established standard model for cosmology and prospects for considerable additions from work in progress. I offer a list of elements of the standard model, comments on controversies in the interpretation of the evidence in…
This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…