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Meaning of a Flat, Open, and Closed Universe 
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#19
Feb113, 10:00 AM

Sci Advisor
P: 4,802

Instead what we do is take many different observations, which are usually some form of correlating redshift with distance, and using the fact that the observed distance depends upon the spatial curvature. With enough such observations at different redshifts, we can obtain constraints on all of the parameters that make up these models (in this case, the parameters are primarily the dark energy density, the total matter density (normal + dark), and the expansion rate, with curvature being determined by the relationship between the total energy density and the expansion rate). The CMB is a bit different, because the overall densities of normal and dark matter also impact the nature of the sound waves in the early universe that set up the pattern of hot and cold spots that we see. Max Tegmark has a selection of movies that show how the various cosmological parameters impact the pattern of hot and cold spots: http://space.mit.edu/home/tegmark/movies.html (The plot shown here is a plot of the "power spectrum" of the CMB, which is the average amplitude of oscillations of a particular size on the sky. Longwavelength oscillations are on the left, shortwavelength oscillations are on the right. The biggest peak is close to one degree on the sky, which means that most of the variation from place to place on the CMB occurs at one degree scales, but there are variations on all scales and the detailed pattern has a lot of power to constrain cosmological variables.) 


#20
Feb313, 10:54 AM

P: 246

Anyhow, thank you for your patience. 


#21
Feb413, 08:18 AM

P: 5,632

dchartier: As you can tell from the discussion above, one question leads to another to another......
Here is an visual illustration of shapes of the universe from NASA and some introductory discussion you may find helpful: http://map.gsfc.nasa.gov/universe/uni_shape.html And another nice introductory source is here: http://www.astro.ucla.edu/~wright/cosmo_03.htm have fun. 


#22
Feb413, 08:33 AM

P: 5,632

Minkowski geometry adds TIME as a fourth dimension to three of space creating SPACETIME....but still flat, no gravity.... http://en.wikipedia.org/wiki/Minkowski_geometry This is where you often see lightcones like those pictured in the above link. You might want to make a mental note that the lightcone traces out what turns out to be a type of 'horizon'...similar to those encountered in GR as that of a black hole for example. Horizons in cosmology are REALLY fun, but not so easy to understand at first. In general relativity, things like pressure, energy and mass CURVE SPACETIME. At slow speeds, say the earth rotating around the sun, or the moon about the earth, even our space probes, most of the 'spacetime curvature' is the curvature of time. And that's VERY close to Newtonian descriptions and is why most spaceflights use Newtonian calculations. For a real world application of GR, check Wikipedia about the GPS satellite system to get a feel for how TIME corrections are necessary due to relativistic effects: satellite time and earth surface time tick at different rates and those differences must be corrected for accurate positioning! 


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