# Meaning of a "Flat," "Open," and "Closed" Universe

by dchartier
Tags: flat, meaning, universe
P: 4,596
 Quote by timmdeeg How do we calculate the spatial geometry from this (whereby I suspect that the measured angle βexp does not coincide with β1, β2 resp.)?
I general it's a multiparamter fit. There is no single calculation that people do. The triangle analogy is more or less a way of understanding how the experiments inform about the curvature, but this doesn't actually correspond to anything cosmologists do.

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. Long-wavelength oscillations are on the left, short-wavelength 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.)
P: 164
 Quote by Chalnoth 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).
Okay, that's very good to know. I have terribly underestimated this complexity. To figure that out is far beyond my scope. And I guess the questions in my last post are too naive to allow a simple answer or are misled regarding this context.

Anyhow, thank you for your patience.
 PF Patron P: 5,492 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.
PF Patron
P: 5,492
 Does this mean that the space-time of the universe is described by Euclidean geometry?
I did not see an answer above....so briefly, Euclidean geometry describes space and the implicit assumption is that the speed of light is infinite....it's flat SPACE.

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 light-cones like those pictured in the above link. You might want to make a mental note that the light-cone 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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