Slashdot Mirror
Universe is Flat
D Anderson n'Swaart writes: "BBC News is reporting that a recent experiment called Project Boomerang, conducted with a super-sensitive telescope suspended 40 km above Antarctica, has provided powerful new evidence to support the current trend in scientific thinking that the fabric of space is essentially flat, and not curved as Einstein postulated. The one billion measurements gathered took three weeks to analyse on a Cray T3E supercomputer, and have provided insights on the creation of the universe, and suggest that it will continue to expand indefinitely without collapsing in a Big Crunch."
Rather, what it means is this: Einstein's theory predicts that spacetime is curved. However, some curved spacetimes can be sliced up into "space" and "time" in such a way that SPACE is flat. Current scientific thinking is that SPACE is flat in this way (or very close to it) -- spacetime is still curved and the curvature obey's Einstein's equation.
Of course, it is true that Einstein personally favored a closed universe model in which space is hyperspherical and hence curved, so in that respect the above statement is correct. But Einstein's theory admits many other solutions and experiments favor near-flatness.
You seem to be confusing two issues: (i) the 'average' flatness of the universe, and (ii) the cosmological constant.
The question of the flatness of the universe question is basically this: if you defined a triangle of geodesics, would the angles in the corners add up to more than 180 degrees (positive curvature: a 2d analogy would be the surface of a sphere); less than 180 degrees (negative curvature, cf the 2d surface of a saddle); or exactly 180 degress (like a 2d sheet of paper).
It turns out, when you do the sums, that an 'empty' expanding universe would not be flat, but would have negative curvature: two geodesics emerging from a point are pulled away from each other. For an expanding universe to be flat, there has to be enough gravitation attraction to balance this pulling apart. If the average energy density is a little higher, the attraction becomes more important than the divergence, leading to positive curvature and a closed universe.
These latest results confirm that the universe appears to be either exactly or very nearly flat. This implies that the average energy density is either exactly or very nearly at the critical value. But the amount of visible matter seems to be too small to account for this. So it has been suggested that there is either more mass in the universe than we can see - "dark matter" - or that empty space itself has an energy density (like a quantum particle's zero-point energy). The present results, by indicating that space is flat, tend to support this idea of a missing energy density. This leads to an extra term in the equations, the Cosmological Constant (Lambda), which appears in addition to the energy density terms arising from visible matter and radiation. A flat universe suggests that Lambda is not zero.
"on average" flat
Strictly speaking, the discussion above assumes a Friedmann model of the universe. This is a simplified model which assumes that the universe is and remains homogeneous -- the same everywhere, with the same density at every point. Normally in relativity there is no way to say whether events in different places are happening at the same time; but in the Friedmann universe one can use the local density of matter (which is the same everywhere) to define a universal "proper time" co-ordinate. Having nailed down the co-ordinate system, one can then separate the spatial and the temporal aspects of the equations.
Of course, the universe is not homogeneous when you look at it closely -- every so often you come across a planet or a star or a black hole; and getting too close to the latter can bend geodesics a lot (gravitational lensing). Nobody is suggesting anything but that the universe is curved "up-close". But on a larger length scale the Friedmann approximation seems to work well: very few geodesics will actually pass close by a black hole; most will indeed experience an "average" amount of bending.
Other information on this project can be found here, here (Caltech), or here. This link to Princeton University seems to explain the project much better, at least to me.