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Question
After seeing Science programs on TV and reading articles, it seams that the Universe will just keep expanding as their is not enough matter to make a big Crunch. My question is, do we know what shape the Universe is. If not then how can we know that all matter will not come back together at a different place. ie if the Universe is flat and is expanding around a sphere it will continue to grow and return the other side ?
Hello,
 geometry','Geometry conforming to accelerated expansion and k= -1 curvature'))
Your explanation (or interpretation) of why there won't be a "big Crunch" is one way to think of it. Another is that the existence of dark energy ensures the universe will accelerate in its expansion and spread out beyond the capability of any deceleration or fallback leading to compression.
An excellent and readable account can be found in: 'Supernovae, Dark Energy and the Accelerating Universe', by Saul Perlmutter, in Physics Today, April, 2003, p. 53.
Specifically the term (rho + 3p) acts as a source of gravity in general relativity, (where rho = energy density).
If we set: 0 = (rho + 3p) then:
p = -rho /3 (or rho = - 3p)
and if: p < (rho/3) we have gravity that repels
In other words, the acceleration of expansion that prevents a big crunch is due to *repulsive gravity*.
Now, universes that re-collapse (decelerate), expand forever with zero limiting velocity (e.g. v uniform) or expand forever with positive limiting velocity (accelerate) are called respectively: 'closed' (can have curvature k = +1); 'critical'-'flat' (k=0) or 'open'-'negative' (can be k = -1), respectively.
Given this, we acknowledge the geometry can neither be spherical or flat (which doesn't comport with the accelerated expansion), but rather "open" or negatively curved in a Lobachevskian- non-Euclidean sense. (I attached an image to show this).
So, no, we are fairly sure - unless the acceleration is suddenly reversed - that there won't be any re-collapse!
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Philip A. Stahl
Expertise
I specialize in stellar and solar astrophysics. Can answer any questions pertaining to these areas, the spectroscopic analysis of stars – as well as the magneto-hydrodynamics of sunspots and solar flares. Sorry – No homework problems done or research projects! I will provide hints on solutions.
Experience
Have published papers on the relationship between sunspot morphology and solar flares; discovery of SID flares related to this, constructed computerized stellar models; MHD research.
Organizations
American Astronomical Society (Solar physics and Dynamical astronomy divisions), American Geophysical Union, American Mathematical Society, Intertel.
Publications
Solar Physics, Journal of the Royal Astronomical Society of Canada, Journal of the Barbados Astronomical Society, Meudon Solar Flare Proceedings (Meudon, France). Books: 'Selected Analyses in Solar Flare Plasma Dynamics', 'Physics Notes for Advanced Level'.
Education/Credentials
B.A. degree in Astronomy; M.Phil. degree in Physics - specializing in solar physics.
Awards and Honors
Postgraduate research award- Barbados government; Studentship Award in Solar Physics - American Astronomical Society
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