## What is a "flat" universe?

Hi

I read about the different shapes that are postulated for the shape of the universe. But what is meant by a "flat" universe? Is it the shape of a sheet, or blanket? If it is, why would the universe expand in suck a manner? It doesn't seem to make sense that it would be huge in 2 dimensions, but be so small in the other.
 No, a flat universe is a Euclidean universe. That essentially means that it obeys the laws of Euclidean geometry, and has no overall energy. This is how you intuitively think about the universe - the angles of a triangle add up to 180 degrees, parallel lines stay parallel, etc.
 Recognitions: Gold Member And to add one more thing, we do NOT know for sure that the universe is flat, but it IS flat to within our ability to measure it (which as I recall is only to about 2% or 3%, so nowhere near 0% curvature), but it would be QUITE an amazing coincidence if the universe, out of all the infinite range of curvature it could take on, just happened to be VERY CLOSE to flat, but not actually flat.

## What is a "flat" universe?

 Quote by phinds And to add one more thing, we do NOT know for sure that the universe is flat, but it IS flat to within our ability to measure it (which as I recall is only to about 2% or 3%, so nowhere near 0% curvature), but it would be QUITE an amazing coincidence if the universe, out of all the infinite range of curvature it could take on, just happened to be VERY CLOSE to flat, but not actually flat.
Hmmm, why is that amazing? It's like saying that to get a round numbered value for a measurement is amazing. We had and experiment where a measured value was 400.0, everyone said it must be a mistake. Isn't it just as likely as any other measurement?

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 Quote by cosmik debris Hmmm, why is that amazing? It's like saying that to get a round numbered value for a measurement is amazing. We had and experiment where a measured value was 400.0, everyone said it must be a mistake. Isn't it just as likely as any other measurement?
I don't agree at all. This is NOT just any number. The ramifications of a flat universe are very significant so "close but no cigar" just seems a little weird.
 Recognitions: Science Advisor To add to it, to get the flatness we now observe in the universe, the earlier universe had to be flat to something like 1 part in 10^60. Perhaps that makes the coincidence a little more pronounced :)

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 Quote by cosmik debris Hmmm, why is that amazing? It's like saying that to get a round numbered value for a measurement is amazing. We had and experiment where a measured value was 400.0, everyone said it must be a mistake. Isn't it just as likely as any other measurement?
So you don't think that a perfectly flat universe would require some explaining? You don't think that such an observation would be telling us something fundamental about the underlying physics? If not, then you would have to content yourself with the fact that the universe is perfectly flat simply by chance. Of course, that could be the case, but it is not a satisfactory way to explore the nature of the universe because some things do need further explaining.

One example is the smoothness of the CMB temperature. We observe that the temperature of the CMB is essentially the same regardless of which direction we look; this means that photons coming from different regions of the universe that were causally disconnected when the CMB was generated have the same temperature. One could simply say, "ehh, whatever. It could have been like that by accident." Or one could try to explain how the homogeneity might be achieved seemingly acausally in the early universe. The former stance would have led to no further development in the field of cosmology; the latter would have led one to the idea of the inflationary universe.

 Quote by cosmik debris Hmmm, why is that amazing? It's like saying that to get a round numbered value for a measurement is amazing. We had and experiment where a measured value was 400.0, everyone said it must be a mistake. Isn't it just as likely as any other measurement?
Cosmik, I maybe wrong in this so someone else maybe able to confirm / deny, but one of the things about the measurement is that there are no metrics associated with the result (it is not like the 400.0 heat / length / volume / weight result of your experiment). Imagine measuring the ratio of heat in ... an apple and comparing it to the heat in ... a planet and finding a result of 0.000....1 - you would be inclined to suggest that there must be a relationship between the two bodies and want to understand what that relationship is. Likewise, a result of 0.000...1 associated with flatness, leads one to think ... this must be telling me something - what might it be telling me?

Regards,

Noel.

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 But what is meant by a "flat" universe? Is it the shape of a sheet, or blanket?
no curvature. yes, flat like a plywood sheet....but really, really, really, BIG.

Article and illustration here:

http://en.wikipedia.org/wiki/Shape_of_the_Universe

 The Wilkinson Microwave Anisotropy Probe (WMAP) has confirmed that the observable universe is flat with only a 0.5% margin of error....
But we can observe only a tiny, tiny portion of the entire [global] universe.

Note that while we model the entire universe using the Friedman-Roberston-Walker model, the uniform and isotropic characteristic assumptions still allow a constant curvature. We assume that model is close enough to represent our observable universe by picking parameters that make it closeto observations. It's the density parameter, omega, that determines curvature. But that model does not work for galactic and even smaller solar system scales....too many lumpy stars and plants on those 'small' scales..so spacetime gets bumpy [gravitational curvature] ....and more so near black holes, neutron stars, and dense planets.

 Quote by phinds And to add one more thing, we do NOT know for sure that the universe is flat, but it IS flat to within our ability to measure it (which as I recall is only to about 2% or 3%, so nowhere near 0% curvature), but it would be QUITE an amazing coincidence if the universe, out of all the infinite range of curvature it could take on, just happened to be VERY CLOSE to flat, but not actually flat.
It's that excactly how it should be? Considering our Observable Universe is so tiny compared to the total universe, shouldn't it appear flat no matter what is the actual shape of the total universe?

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 Quote by Octavianus It's that excactly how it should be? Considering our Observable Universe is so tiny compared to the total universe, shouldn't it appear flat no matter what is the actual shape of the total universe?
No, I don't see why it should be, and how about Nabeshin's post. Did you read it?