![]() ![]() The universe is open with negative curvature the density parameter ![]() Thus, if the universe is flat (contains just theĪmount of mass to close it) the density parameter is exactly 1, if Universe to the critical density that would be required to cause theĮxpansion to stop. Parameter", which is defined as the ratio of the actual density of the The geometry of the universe is often expressed in terms of the "density Thus, at some point in the future the galaxies will stop receding from each other and begin approaching each other as the universe collapses on itself. The expansion will eventually stop and turn into a contraction. The universe in this case is not infinite, but it has no end (just as the area on the surface of a sphere is not infinite but there is no point on the sphere that could be called the "end"). If space has positive curvature, there is more than enough mass to stop the present expansion of the universe. That we learn in high school is called Euclidian geometry). This is termed a flat universe or aĮuclidian universe (because the usual geometry of non-curved surfaces Thus, the universe has no bounds and will also expandįorever, but with the rate of expansion gradually approaching zeroĪfter an infinite amount of time. If space has no curvature (i.e, it is flat), there is exactlyĮnough mass to cause the expansion to stop, but only after an infiniteĪmount of time. If space has negative curvature, there is insufficient mass toĬause the expansion of the universe to stop. So what do the three types of curvature - zero, positive, and negative -mean to the universe? This IS difficult to visualize! Nevertheless, it can be described mathematically by the same methods that mathematicians use to describe the 2-dimensional surfaces. The preceding is not too difficult to visualize, but General Relativity asserts that space itself (not just an object in space) can be curved, and furthermore, the space of General Relativity has 3 space-like dimensions and one time dimension, not just two as in our example above. The flat surface at the left is said to have zero curvature, the spherical surface is said to have positive curvature, and the saddle-shaped surface is said to have negative curvature. Mathematicians distinguish 3 qualitatively different classes of curvature, as illustrated in the following image: Universe, and each implies a different past and future for the universe.įirst, let's look at shapes and curvatures for a two-dimensional surface. Each of these possibilites is tied to theĪmount of mass (and thus to the total strength of gravitation) in the If space itself is curved, there are three general possibilities for the Have their paths deflected, exactly as if a force had acted on them. One of the most profound insights of General Relativity was the conclusionĬaused space to curve, and objects travelling in that curved space What is the shape of the universe? StarChild Question of the Month for July 2001 Question: ![]()
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