Is the universe flat? There are more than one way to view the description of the universe as flat. There is the description of an open, flat or closed universe in terms of it's fate, expansion forever away from gravity, or a big crunch.
Then there is the description of our observable universe being flat in it's geometry, or is it that there is no way to measure the tiny curve of space in our part of the sphere.
Another probably wrong idea is that the entire universe is flat. Are these things confused, even by the experts?
 A: It is only in the absence of dark energy that the correspondence between geometrical curvature and the ultimate fate of the universe is as straightforward as you describe.
Measurements (primarily of the cosmic microwave background) indicate that our universe is flat or very nearly so, which should be interpreted geometrically (i.e. in terms of the sum of the angles of a geodesic triangle). In the absence of dark energy, this would correspond to a scenario in which the universe continued to expand but asymptotically approached zero expansion velocity. 
However, the concurrent measurements of the presence dark energy suggest that our geometrically flat universe will continue to undergo accelerated expansion. 
The influence of dark energy is sometimes neglected in popular accounts, leading to much confusion among non-experts. Keep in mind, though, that it was only in the last 15 years or so that scientists had any direct evidence for the presence of dark energy, so it might be understandable why it was put aside in earlier simplified explanations.
A discussion of the ultimate fate of the universe, its connection to geometrical curvature, and the role of dark energy, is found in the wiki article. 
A: There's a difference between curvature of spacetime and curvature of space.
Extrapolating from what we can see around us and assuming the cosmological constant lives up to its name, spacetime will eventually approach curved de Sitter geometry, in contrast to flat Minkowski geometry or anti-de Sitter geometry of opposite curvature. This is something of an idealization: Obviously, we can't really know what goes on beyond the cosmic event horizon, and the cosmological constant might not deserve its name.
Taking the preferred spatial slicing at constant cosmological time into account, we can also talk about spatial curvature. It turns out the universe is spatially flat (or very nearly so). However, this does not tell us if the universe is spatially compact or infinite - eg a torus can be equipped with a flat connection in spite of being compact.
A: I think this is an example,universe is rotating about its own central axis.if this is the case,take a curve beaker and a flat plate with some water in them.First shake clockwise the curved beaker and then flat plate.In which,beaker or plate did the circular motion was seen about its center?I guess curved one.So,our universe is curved.
