infinite universe (idea)
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Statements about cosmology should be based on science. All ontological arguments aside, it's becoming more and more apparent that the universe is indeed infinite, with an inifnite amount of matter and energy. Scientists are led to this by current theories of physics and astronomical observations.
After I originally posted this, I argued this subject back and forth via /msg with various noders for several weeks. I was forced to go back and make sure that I remembered the cosmology I learned so long ago correctly. It turns out I had, with a big however at the end.
In the early 20th century, Albert Einstein's theory of General Relativity showed that matter curves the space around it. Our idea of space in the Universe as a whole is a 3-manifold embedded in a larger spacetime. This is really a matter for another node1, but we will touch on it later.
Meanwhile, one interpretation of Einstein's theory was that the universe was continually expanding (which Einstein disliked so much that he threw a fudge factor called the "cosmological constant" into the theory to get rid of it). The universe's expansion became widely accepted after Edwin Hubble's observation of red shift in almost every other galaxy in the late 1920's, and confirmed by the observation of cosmic microwave background radiation of Arno Penzias and Robert Wilson in the early 1960's.
So, physicists were led to one of two possibilities:
The density of matter in the Universe determines not only its fate, but also its size. Strangely enough, it is an inverse relation.
Unexpectedly, it has been recently observed that the expansion of the Universe is speeding up. The cosmological constant has been resurrected as an idea, but we are also forced to discard the possibility of a closed universe. Without some new physics, we will have to accept the idea of a forever-expanding, open, infinite universe.
There are two flies in our ointment that may lead to "new physics":
There is an important valid objection to the picture I've painted above, which has to be addressed: A universe that expands forever doesn't necessarily have to be infinite in extent to start with (if it wasn't to start with, it never will be). If we delve into the subject matter of Which 3-manifold do we live in? and Which 4-manifold do we live in?, 3-D slices of the Universe for particular points in time could possibly be compact (= finite for our purposes) even if the slices extend forever. It is possible that we are embedded in some sort of 4-dimensional hypercone or hypertrumpet.
All of that said, the standard model of cosmology still portrays an open universe as spatially infinite at any given point in time. According to General Relativity, the curvature of space (determined by the matter embedded in it) controls its shape. A closed universe has negative curvature; an open universe has zero or negative curvature.
While our hypertrumpet and hypercone have negative curvature in timelike directions, they both have positive curvature in spacelike directions. An infinite volume is still the only 3-manifold with zero curvature (and an infinite hyperbolic paraboloid is still the only manifold with negative curvature) explained by General Relativity alone.
It turns out that compact hyperbolic manifolds (such as the Weeks Space) exist. A 3-torus would work in a flat universe. But then, we would have to live in a universe with a really funky topology (I should have read Which 4-manifold do we live in? first). However, results from the Wilkinson Microwave Anisotropy Probe seem to indicate that the universe is flat.
Another objection: An infinite amount of matter will result in an infinite gravitational pull. There are a couple of possible ways out of this, all hinging on the observed fact that the Universe is expanding:
1Please read Which 3-manifold do we live in? and Which 4-manifold do we live in?