The standard CDM model of cosmology assumes the Copernican principle, which states that the Universe is isotropic and homogeneous on large scales.

2. topologically trivial (not periodic within 3000 Mpc). Using a sphere in standard cosmology is what is done because was have every reason to believe the universe is homogeneous and isotropic at every point. of the Universe is strongly disfavoured, with odds of 121,000:1 against. The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity.They were first derived by Alexander Friedmann in 1922 from Einstein's field equations of gravitation for the Friedmann–Lemaître–Robertson–Walker metric and a perfect fluid with a given … In physics, a homogeneous material or system has the same properties at every point; it is uniform without irregularities. The universe observed The observed universe has the following properties: 1. homogeneous and isotropic when averaged over the largest scales (homogeneous means isotropic from every vantage point). Being non-isotropic would mean there is a preferred direction in space, for example, if the entire universe were rotating. However, going back to the theorists and the torus, if the torus was big enough, really really big enough, it would appear homogeneous and isotropic to creatures living on it because they can't see far enough away to see … There is a problem with the question, in that “homogenous” and “isotropic” are RELATIVE approximations of “something” that can’t possibly exist, EXCEPT in either an “unbounded”, an “infinitesimal”, or an “infinite” domain. It would be a weird place. 4. hotter in the past, cooling (CMB). B. Then the axis of rotation is a special direction. A uniform electric field (which has the same strength and the same direction at each point) would be compatible with homogeneity (all points experience the same physics). 3. expanding (Hubble ow). While the universe does seem to be approximately homogeneous and isotropic, studies such as this are hinting that it isn’t exact. LecturesonCosmology Lecturer: Jo Dunkley Lecture notes from: Pedro G. Ferreira Astrophysics, University of Oxford, DW Building, Keble Road, Oxford OX1 3RH, UK last modified January 5, 2016 1 HomogeneousandIsotropicSpace-Times In these lectures we will focus on one set ofsolutions tothe Einstein Field Equations which apply in a very particular regime. Study of Homogeneous and Isotropic Universe in Gravity M. Sharif 1 and Aisha Siddiqa 1 1 Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan