What is the shape of the Universe?

v. 3 n. 13

Impressive problem statement (skipping to next paragraph recommended): "Shape of the universe : What is the 3-manifold ?of?comoving space , i.e., of a comoving spatial section of the universe, informally called the "shape" of the universe? Neither the curvature nor the topology is presently known, though the curvature is known to be "close" to zero on observable scales. The?cosmic inflation ?hypothesis suggests that the shape of the universe may be unmeasurable, but, since 2003,?Jean-Pierre Luminet , et al., and other groups have suggested that the shape of the universe may be the?Poincaré dodecahedral space . Is the shape unmeasurable; the Poincaré space; or another 3-manifold?" *

Translation of "Impressive problem statement": The above premise that the Universe is a "3-manifold" can prejudice a study and is regarded subsequently. Retaining the notion of continuity, though -- no gaps, ends, edges, "multiverse" (discussed previously) -- but beginning with an ideal one-dimensional space:

1. a one-dimensional continuous entity can be an infinitely long, infinitesimally thin straight line -- a finite straight line has a discontinuity on each end unless it was joined by means of another dimension into a circle;
2. two-dimensional, infinite flat surface -- unless joined by means of a third dimension into a hollow finite form with infinitesimally thin skin;**
3. three-dimensional, infinite volume -- any smooth joining of a finite volume of space by means of another space dimension into a smooth four-dimensional entity would be a purely mathematical extension; only three space dimensions are available to physical examination.

It is observed that a light ray "curves" toward the Sun because of the distortion of space due to the high mass of the Sun according to general relativity. On the other hand, in optics, when a ray of light passes from a less dense to more dense medium, the ray bends toward the more dense:

A conundrum arises, though, with the conventional thought-picture of "curvature" because when looking deeply into the Universe, space looks "flat," even though the mass of the Universe seems to be some 10^50 kilograms. One would think it would be "curved" because of all that mass.? But curved relative to what? A type of "giant sun" outside the Universe? Curved relative to itself? This could imply finiteness, but according to the "no necessary 3-manifold condition" and Item 3 above there are no more space dimensions to maneuver in. In general relativity there are only three space dimensions; the fourth is time. Therefore space at large should not be expected to "curve" into a fourth space dimension. "Curved" conventionally suggests transverse distortion, but curved might also mean longitudinal distortion, which might not be visible when viewing deeply into space, i.e., the cosmological principle of uniformity on sufficiently large scales.

Another interpretation of "curvature" was introduced, where the fourth dimension is expansion/contraction of the familiar three space dimensions (longitudinal distortion), because space is observed to be undergoing accelerated expansion, and this has to be from a more contracted or compressed state of higher potential energy. Compression of the medium indicates greater density. The space near the Sun, then, might be described as being more dense than away from the Sun -- possible refraction of light ray toward the Sun, as observed, as in the illustration with air and water, less to more dense medium. ?

Regarding the Universe at large, the cover image indicates the observer at the center viewing two light rays from about the beginning of the known Universe. The rays are straight, as observed with current instrumentation, given longitudinal rather than transverse distortion of light rays from homogeneous space. This is also an explanation for the unlikely fine balance between conventional "positive and negative curvature" of 3-manifolds, or just the so-called "unlikely right amount of visible matter to produce a flat 3-manifold." The mathematics of the conventional 3-manifold supposition, then, could be misleading.

So, what is the shape of the Universe? Perhaps infinite flat three-dimensional space with at least one region more contracted than usual that we call the observable Universe.

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* https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics#Cosmology_and_general_relativity

** Beginning with an infinite flat surface and shaping a finite form, also shapes an infinite space less this finite form on the other side of the surface.

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