Shape of The Universe - Introduction

Introduction

Consideration of the shape of the universe can be split into two:

1. local geometry, which relates especially to the curvature of the universe, especially in the observable universe, and
2. global geometry, which relates to the topology of the universe as a whole, measurement of which may not be within our ability.
   

If the observable universe encompasses the entire universe, we may determine the global structure by observation. If the observable universe is smaller than the entire universe (in some models it is many orders of magnitude smaller or even infinitesimal), observation is limited to a part of the whole. Possibly the universe is small in some dimensions and not in others (like a cylinder). If it were a small closed loop, one would see multiple images of an object in the sky, although not necessarily of the same age.

Cosmologists normally work with a given space-like slice of spacetime called the comoving coordinates, the existence of a preferred set of which is possible and widely accepted in present-day physical cosmology. The section of spacetime that can be observed is the backward light cone (all points within the cosmic light horizon, given time to reach a given observer), while the related term Hubble volume can be used to describe either the past light cone or comoving space up to the surface of last scattering. To speak of "the shape of the universe (at a point in time)" is ontologically naive from the point of view of special relativity alone: due to the relativity of simultaneity we cannot speak of different points in space as being "at the same point in time" nor, therefore, of "the shape of the universe at a point in time".