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Strictly speaking, however, the FLRW equation applies to a smooth and homogeneous universe. So to calculate the scale factor at each step, cosmologists typically assume the universe is smooth and use its average density--determined from the simulation--as the FLRW metric's input. That's a bit dicey, because general relativity says that mass and energy warp spacetime. As a result, space should expand faster in emptier regions and slower in crowded ones, where the galaxies' gravity pulls against the expansion. Thus, in principle, inhomogeneities in the universe can feed back through the dynamics and affect the universe's expansion.

Gábor Rácz and László Dobos, astrophysicists at Eötvös Loránd University in Budapest, and their colleagues set out to capture that "backreaction." They simulated a cube of space measuring 480 million light-years along each side. Instead of using the FLRW metric to calculate at each time step a single scale factor for the entire cube, they broke the cube into 1 million miniuniverses and then used the equation to calculate the scale factor in each of them. "We assume that every region of the universe determines its expansion rate itself," Dobos says. The researchers then calculated the average of the many scale factors, which can differ from the scale factor calculated from the average density.

The team's virtual universe evolved much as the real one has, with its expansion accelerating over the past few billion years. That happened even without adding space-stretching dark energy to the simulation, the researchers report in a paper in press at the Monthly Notices of the Royal Astronomical Society. The results suggest that it may be possible to explain away dark energy as an illusion, Dobos says.

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