The large scale geometry of the universe is governed by Einstein's General Theory of Relativity. Einstein showed that gravity curves three-dimensional space, and that space in turn moves matter. For the universe as a whole, the shape of the curvature depends on the average density of the matter. If the average density of matter in the universe is greater than the critical density, the force of gravity will eventually rein in expansion and cause the universe to collapse upon itself. In this case, the universe is said to be positively curved, and Omega, the ratio of the average density to the critical density, is greater than 1. Conversely, if the average density of matter in the universe is less than the critical density, gravity will lose its grip on matter and the universe will expand forever. This negatively curved universe is defined by an Omega less than one. If Omega is exactly one--that is, if the average density of the universe is equal to the critical density--then the universe will expand to a maximum density and remain there for eternity. This universe is flat; it has zero curvature. Now three dimensional curved space is difficult to visualize, but we can illustrate the curvature in two dimensions. A positively curved universe is like the surface of a sphere; a negatively curved universe, like a saddle. A universe with zero curvature is, not surprisingly, like a plane. If you could draw a triangle by reaching far enough into space to draw lines connecting three far-flung galaxies, you could determine the curvature of the universe. The angles of a triangle in a negatively curved universe would add to greater than 180 degrees; those of a triangle in a positively curved universe, to less than 180 degrees. In a flat universe, familiar Euclidean geometry applies, and the angles of the triangle add up to exactly 180 degrees.

This is a question answer sight from the site http://imagine.gsfc.nasa.gov/docs/ask_astro/ask_an_astronomer.html
Written by Paul Butterworth for the Ask a High-Energy Astronomer team

How big is the Universe and how is it measured?

The simple answer is that the observable Universe is about 10 billion light years in radius. That number is obtained by multiplying how old we think the Universe is by the speed of light. The reasoning there is quite straightforward: we can only see out to that distance from which light can have reached us since the Universe began. (But see my note marked * below).

We determine the age of the Universe in a number of ways. One is to estimate the age of the oldest stars we see. Our knowledge of how stars of a given size evolve with time is very good (based on what we know about atomic and nuclear physics) so the major uncertainty here is usually measuring how far away (and so how big) such stars are. The standard method is to look for very small changes in the apparent positions of the stars as the Earth moves around the Sun. (This effect is called parallax). A second way to get an age for the Universe is to try to figure out the time of the big bang itself. Here the method is to use a series of techniques (based on how bright things appear to be - like Cepheid variable stars - that we think we know the true brightness of) to determine first the distance of the nearby galaxies, then increasingly distant galaxies, until we have estimated distances for many galaxies for which relative velocity measurements have been made (using the Doppler red shift of features in their spectra). The relative velocities we observe for distant galaxies have been largely determined by the expansion of the Universe begun with the 'big bang'. So, once we've determined how expansion velocity correlates with distance for some range of distances, it's possible to extrapolate back (with some assumptions) to calculate the instant of the big bang, when all the matter in the Universe was at a single point.

The determination of greater and greater distances is one of the great themes of astronomy. Most introductory books will give you an outline of the story, which you can then fill in to any level of detail with further reading.

Our website has a lot of material on recent developments. For instance, there are already several answers in the 'Ask a High-Energy Astronomer' archive which deal with the size and age of the Universe. If you enter things like 'size of the Universe', 'age of the Universe', or 'distance scale' in our search window you will get lists of links to many of the most relevant discussions.

Paul Butterworth
for the Ask a High-Energy Astronomer team

* Note: The observable Universe may be only a small part of the physical Universe. In some theories, the Universe may have expanded very fast just after the 'big bang', and only a little bit may have remained within range of detection.

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