*Template design only.* The shape of the universe is a matter of debate within physical cosmology over the geometry of the universe including both local geometry and global geometry. It is loosely divided into curvature and topology, even though strictly speaking, it goes beyond both. More formally, the subject in practice investigates which 3-manifold corresponds to the spatial section in comoving coordinates of the 4-dimensional space-time of the Universe.

Throughout recorded history, several cosmologies and cosmogonies have been proposed to account for observations of the universe. The earliest quantitative geocentric models were developed by the ancient Greeks, who proposed that the universe possesses infinite space and has existed eternally, but contains a single set of concentric spheres of finite size — corresponding to the fixed stars, the Sun and various planets — rotating about a spherical but unmoving Earth. Over the centuries, more precise observations and improved theories of gravity led to Copernicus's heliocentric model and the Newtonian model of the Solar System, respectively. Further improvements in astronomy led to the realization that the Solar System is embedded in a galaxy composed of billions of stars, the Milky Way, and that other galaxies exist outside it, as far as astronomical instruments can...

*Template design only.* Throughout recorded history, several cosmologies and cosmogonies have been proposed to account for observations of the universe. The earliest quantitative geocentric models were developed by the ancient Greeks, who proposed that the universe possesses infinite space and has existed eternally, but contains a single set of concentric spheres of finite size — corresponding to the fixed stars, the Sun and various planets — rotating about a spherical but unmoving Earth. Over the centuries, more precise observations and improved theories of gravity led to Copernicus's heliocentric model and the Newtonian model of the Solar System, respectively. Further improvements in astronomy led to the realization that the Solar System is embedded in a galaxy composed of billions of stars, the Milky Way, and that other galaxies exist outside it, as far as astronomical instruments can reach. Careful studies of the distribution of these galaxies and their spectral lines have led to much of modern cosmology. Discovery of the red shift and cosmic microwave background radiation revealed that the universe is expanding and apparently had a beginning.

Careful studies of the distribution of these galaxies and their spectral lines have led to much of modern cosmology. Discovery of the red shift and cosmic microwave background radiation revealed that the ...

*Template design only.* Given gravitation's predominance in shaping cosmological structures, accurate predictions of the universe's past and future require an accurate theory of gravitation. The best theory available is Albert Einstein's general theory of relativity, which has passed all experimental tests hitherto. However, since rigorous experiments have not been carried out on cosmological length scales, general relativity could conceivably be inaccurate. Nevertheless, its cosmological predictions appear to be consistent with observations, so there is no compelling reason to adopt another theory.

General relativity provides a set of ten nonlinear partial differential equations for the spacetime metric (Einstein's field equations) that must be solved from the distribution of mass-energy and momentum throughout the universe. Since these are unknown in exact detail, cosmological models have been based on the cosmological principle, which states that the universe is homogeneous and isotropic.

In effect, this principle asserts that the gravitational effects of the various galaxies making up the universe are equivalent to those of a fine dust distributed uniformly throughout the universe with the same average density. The assumption of a uniform dust makes it easy to solve Einstein's field equations and predict the past and future of the universe.

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