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The purpose of this work is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. This paper concentrates on general…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Gordon McCabe

The problems of coarse-graining and averaging of inhomogeneous cosmologies, and their backreaction on average cosmic evolution, are reviewed from a physical viewpoint. A particular focus is placed on comparing different notions of average…

General Relativity and Quantum Cosmology · Physics 2011-08-08 David L. Wiltshire

I start by defining the cosmological parameters $H_0, \Omega_m$ and $\Omega_\Lambda$. Then I show how the age of the universe depends on them, followed by the evolution of the scale parameter of the universe for various values of the…

High Energy Physics - Phenomenology · Physics 2009-10-31 Palash B. Pal

We consider a cosmology in which a spherically symmetric large scale inhomogeneous enhancement or a void are described by an inhomogeneous metric and Einstein's gravitational equations. For a flat matter dominated universe the inhomogeneous…

Astrophysics · Physics 2008-11-26 J. W. Moffat

The question of the averaging of inhomogeneous spacetimes in cosmology is important for the correct interpretation of cosmological data. In this paper we suggest a conceptually simpler approach to averaging in cosmology based on the…

General Relativity and Quantum Cosmology · Physics 2015-05-27 A. Coley , J. Brannlund , J. Latta

Interpretation of cosmological data to determine the number and values of parameters describing the universe must not rely solely on statistics but involve physical insight. When statistical techniques such as "model selection" or…

Astrophysics · Physics 2011-08-31 Eric V. Linder , Ramon Miquel

Usually, we assume that there is no inhomogeneity isotropic in terms of our location in our uni- verse. This assumption has not been observationally confirmed yet in sufficient accuracy, and we need to consider the possibility that there…

Cosmology and Nongalactic Astrophysics · Physics 2017-03-06 Hiroyuki Negishi , Ken-ichi Nakao

We present a brief history of the construction of models of the universe, followed by calculations of quantitative characteristics of basic geometric and kinematic properties of the Standard Cosmological Model ($\Lambda$CDM). Using the…

General Relativity and Quantum Cosmology · Physics 2026-04-23 D. I. Nagirner , S. G. Jorstad , A. V. Dementyev

This thesis concerns the compatibility of inhomogeneous cosmologies with our present understanding of the universe. It is a problem of some interest to find the class of all relativistic cosmological models which are capable of providing a…

Astrophysics · Physics 2007-05-23 Chris A. Clarkson

A cosmological model with total density close to critical (and flat geometry), dominated by dark matter and dark energy of unknown nature, and consistent with the basic predictions of the inflationary scenario is a very good fit to a…

Astrophysics · Physics 2007-05-23 A. Balbi

A nontrivial topology of the spatial section of the universe is an observable, which can be probed for all locally homogeneous and isotropic universes, without any assumption on the cosmological density parameters. We discuss how one can…

Astrophysics · Physics 2008-11-26 M. J. Reboucas

Given the wealth of increasingly accurate cosmological observations, especially the recent results from the WMAP, and the development of methods and strategies in the search for cosmic topology, it is reasonable to expect that we should be…

Astrophysics · Physics 2008-11-26 M. J. Reboucas , J. S. Alcaniz

I review the reason for considering the prime purpose of the program of measurements of the fundamental parameters of cosmology to be the tests of cosmological models. I comment on the philosophy by which we are approaching this goal, offer…

Astrophysics · Physics 2007-05-23 P. J. E. Peebles

This paper presents a general averaging procedure for a set of observers which are tilted with respect to the cosmological matter fluid. After giving the full set of equations describing the local dynamics, we define the averaging procedure…

General Relativity and Quantum Cosmology · Physics 2009-04-22 J. Larena

Over the past three years, our confidence in the inferred values of cosmological parameters has increased dramatically, confirming that the flat matter dominated Universe that dominated cosmological model building for the past 20 years does…

Astrophysics · Physics 2016-11-03 Lawrence M. Krauss

This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous,…

Astrophysics · Physics 2015-06-24 Marcelo B. Ribeiro

A mathematical model of the Universe evolution, based on asymmetric doublet of classical and phantom dcalar Higgs fields with a kinetic connection between the components, has been constructed and studied. A detailed qualitative analysis was…

General Relativity and Quantum Cosmology · Physics 2024-11-26 Yu. G. Ignat'ev , I. A. Kokh

How does inhomogeneity affect our interpretation of cosmological observations? It has long been wondered to what extent the observable properties of an inhomogeneous universe differ from those of a corresponding…

Cosmology and Nongalactic Astrophysics · Physics 2016-12-28 John T. Giblin , James B. Mertens , Glenn D. Starkman

It has recently been proposed [M. P. Hertzberg and A. Loeb, arXiv:2302.09090] that the observed value of the cosmological constant can be related to the physical parameters of the Standard Model. In the present compact note we point out…

General Relativity and Quantum Cosmology · Physics 2023-02-23 Shahar Hod

A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe.…

Cosmology and Nongalactic Astrophysics · Physics 2017-11-07 Siamak Ravanbakhsh , Junier Oliva , Sebastien Fromenteau , Layne C. Price , Shirley Ho , Jeff Schneider , Barnabas Poczos