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# 5.1 Horizon problem

The horizon problem is perhaps the most fundamental problem for cosmology, and arises because of the uniformity of the observed CMB. This uniformity is the result of thermal equilibrium between matter and radiation at the time of last scattering, 380,000 years after the big bang. However, in order for such equilibrium to be possible, transfer of energy needs to be possible across the region being considered – in other words, a region in thermal equilibrium cannot have a size that is larger than the distance a signal can travel at the time being considered (i.e. the acoustic scale).

At a redshift of (corresponding to the epoch noted above), the acoustic scale corresponds to an angular separation of , and so regions on the sky separated by an angular scale of more than this amount should have been outside each other’s horizon distance at the time of last scattering, and therefore not causally connected. Yet we observe that they appear to have been in thermal equilibrium. Postulating a brief period of inflation can solve this problem by rapidly separating regions that were initially in contact and able to come into equilibrium.

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