Flatness problem

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The flatness problem is a cosmological fine-tuning problem within the Big Bang model. 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 flatness problem arises because of the observation that the density of the universe today is very close to the critical density required for spatial flatness.[2]. Since the total energy density of the universe departs rapidly from the critical value over cosmic time,[3] the early universe must have had a density even closer to the critical density, leading cosmologists to question how the density of the early universe came to be fine-tuned to this 'special' value.

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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 \Omega~=~1~\pm~10^{-60}. 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

  1. ^ Barbara Ryden. Introduction to Cosmology. Addison Wesley. 
  2. ^ a b D. N. Spergel et al. (June 2007). "Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology". ApJS 170: 337-408. doi:10.1086/513700. 
  3. ^ Peacock, J. A. (1998). Cosmological Physics. Cambridge: Cambridge University Press. ISBN 978-0521422703.