Flatness problem 1118171 220978508 2008-06-22T14:16:47Z DOI bot 6652755 Citation maintenance. You can [[WP:DOI|use this bot]] yourself! Please [[User:DOI_bot/bugs|report any bugs]]. {{expert-portal|Astronomy}} The '''flatness problem''' is a [[physical cosmology|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 [[cosmic inflation|inflationary universe]]<ref>{{cite book|author = Barbara Ryden|title = Introduction to Cosmology|publisher = Addison Wesley}}</ref>. 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.<ref name="wmap3">{{cite journal|author = D. N. Spergel ''et al.''|title = Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology|year=2007|month=June|journal=ApJS|volume=170|pages=337–408|url=http://adsabs.harvard.edu/abs/2007ApJS..170..377S |accessdate=2007-10-11|doi = 10.1086/513700}}</ref>. Since the total energy density of the universe departs rapidly from the critical value over [[cosmic time]],<ref name="peacock">{{cite book |last= Peacock|first=J. A. |title= Cosmological Physics |year= 1998|publisher=Cambridge University Press |location=Cambridge |isbn= 978-0521422703}}</ref> 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-tuning|fine-tuned]] to this 'special' value. ==Current Universe== The [[dimensionless]] parameter <math>\Omega_0</math> 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 <math>\Omega_0</math> to be 1 within 1%.<ref name="wmap3">{{cite journal|author = D. N. Spergel ''et al.''|title = Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology|year=2007|month=June|journal=ApJS|volume=170|pages=337–408|url=http://adsabs.harvard.edu/abs/2007ApJS..170..377S |accessdate=2007-10-11|doi = 10.1086/513700}}</ref> ==Early Universe== In the early universe <math>\Omega</math> is the ratio of the energy density to the critical density at that time. In the [[Lambda-CDM model|Lambda-CDM]] cosmology favoured by astronomers, the early universe is dominated by [[radiation]], then by [[matter]]. In this case, if <math>\Omega</math> is much greater than 1, the universe quickly recollapses in a [[Big crunch]]. If <math>\Omega</math> is much less than one, the universe expands so quickly that matter cannot collapse under [[gravity]] to form [[galaxy|galaxies]] or [[star]]s. If the current value of <math>\Omega</math> is extrapolated back to the [[Planck time]] the value of <math>\Omega</math> is such that <math>\Omega~=~1~\pm~10^{-60}</math>. 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. ==Inflation== The problem is that a simple big bang theory cannot explain how an <math>\Omega</math> 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. ==References== <div class="references-small"><references /></div> [[Category:Physical cosmology]] [[Category:Cosmic inflation]] [[fr:Problème de la platitude]] [[nl:Vlak heelal]] [[ja:平坦性問題]]