Flatness problem
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The flatness problem is a cosmological fine-tuning problem within the Big Bang model. The problem is that the density of energy in the universe today is very close to the critical density, and extrapolating backwards in time, the energy density of the universe is increasingly closer to the critical density, without any reason why the energy density should be close to the critical density at the time of the Universe's creation. Along with the Monopole problem and the Horizon problem, it is one of the three primary motivations for the theory of an inflationary universe[1]. The name flatness problem comes from the fact that a universe with the critical density has no curvature, and hence is flat.
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[edit] Current Universe
The dimensionless parameter Ω0 measures the ratio of the energy density of the universe to the universe's critical density at the current time. WMAP's third year data, combined with data from the Sloan Digital Sky Survey constrain Ω0 to be 1 within 1%.[2]
[edit] Early Universe
In the early universe Ω is the ratio of the energy density to the critical density at that time. In the Lambda-CDM cosmology favoured by astronomers, the early universe is dominated by radiation, then by matter. In this case, if Ω is much greater than 1, the universe quickly recollapses in a Big crunch. If Ω is much less than one, the universe expands so quickly that matter cannot collapse under gravity to form galaxies or stars. If the current value of Ω is extrapolated back to the Planck time the value of Ω is such that 
. That this value is so close to the critical value when it could take on any value at all is regarded as a highly improbable coincidence.
[edit] Inflation
The problem is that a simple big bang theory cannot explain how an Ω so close to unity could arise. The problem is solved by the hypothesis of an inflationary universe, in which very shortly after the Big Bang, the universe increased in size by an enormous factor. Such an inflation would have smoothed out any non-flatness originally present and resulted in a universe with a density extremely close to the critical density.
[edit] References
- ^ Barbara Ryden. Introduction to Cosmology. Addison Wesley.
- ^ D. N. Spergel, R. Bean, O. Dore', M. R. Nolta, C. L. Bennett, G. Hinshaw, N. Jarosik, E. Komatsu, L. Page, H. V. Peiris, L. Verde, C. Barnes, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weiland, E. Wollack, E. L. Wright (2006). "Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology." 19 March 2006.
