A remarkable finding of the early 21st century, that kind of sits alongside the Nobel prize winning discovery of the universe’s accelerating expansion, is the finding that the universe is geometrically flat. This is a remarkable and unexpected feature of a universe that is expanding – let alone one that is expanding at an accelerated rate – and like the accelerating expansion, it is a key feature of our current standard model of the universe.
It may be that the flatness is just a consequence of the accelerating expansion – but to date this cannot be stated conclusively.
As usual, it’s all about Einstein. The Einstein field equations enable the geometry of the universe to be modelled – and a great variety of different solutions have been developed by different cosmology theorists. Some key solutions are the Friedmann equations, which calculate the shape and likely destiny of the universe, with three possible scenarios:
The Friedmann equations were used in twentieth century cosmology to try and determine the ultimate fate of our universe, with few people thinking that the flat scenario would be a likely finding – since a universe might be expected to only stay flat for a short period, before shifting to an open (or closed) state because its expansion (or contraction) would alter the density of its contents.
Matter density was assumed to be key to geometry – and estimates of the matter density of our universe came to around 0.2 atoms per cubic metre, while the relevant part of the Friedmann equations calculated that the critical density required to keep our universe flat would be 5 atoms per cubic metre. Since we could only find 4% of the required critical density, this suggested that we probably lived in an open universe – but then we started coming up with ways to measure the universe’s geometry directly.
There’s a You-Tube of Lawrence Krauss (of Physics of Star Trek fame) explaining how this is done with cosmic microwave background data (from WMAP and earlier experiments) – where the CMB mapped on the sky represents one side of a triangle with you at its opposite apex looking out along its two other sides. The angles of the triangle can then be measured, which will add up to 180 degrees in a flat (Euclidean) universe, more than 180 in a closed universe and less than 180 in an open universe.
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| Various universe evolution scenarios. A universe with too much density collapses in on itself, a critical density universe stays static, while a universe with not enough density keeps expanding at a steady (coasting) rate. However, today's cosmology puts emphasis upon the cosmological constant, which gives an accelerating expansion. Does this mean that density is irrelevant? [Credit: NASA] |
As usual, it’s all about Einstein. The Einstein field equations enable the geometry of the universe to be modelled – and a great variety of different solutions have been developed by different cosmology theorists. Some key solutions are the Friedmann equations, which calculate the shape and likely destiny of the universe, with three possible scenarios:
- closed universe – with a contents so dense that the universe’s space-time geometry is drawn in upon itself in a hyper-spherical shape. Ultimately such a universe would be expected to collapse in on itself in a big crunch.
- open universe – without sufficient density to draw in space-time, producing an outflung hyperbolic geometry – commonly called a saddle-shape – with a destiny to expand forever.
- flat universe – with a ‘just right’ density – although an unclear destiny.
The Friedmann equations were used in twentieth century cosmology to try and determine the ultimate fate of our universe, with few people thinking that the flat scenario would be a likely finding – since a universe might be expected to only stay flat for a short period, before shifting to an open (or closed) state because its expansion (or contraction) would alter the density of its contents.
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| Although the contents of the early universe may have just been matter, we now must add dark energy to explain the universe's persistent flatness [Credit: NASA] |
There’s a You-Tube of Lawrence Krauss (of Physics of Star Trek fame) explaining how this is done with cosmic microwave background data (from WMAP and earlier experiments) – where the CMB mapped on the sky represents one side of a triangle with you at its opposite apex looking out along its two other sides. The angles of the triangle can then be measured, which will add up to 180 degrees in a flat (Euclidean) universe, more than 180 in a closed universe and less than 180 in an open universe.