There's copious documents about how Inflation solves the problem that General Relativity predicts a lumpy CMB. That influation 'smooths' out the curvature fluctuations and, so, predicts a CMB at thermal equilibrium. The perfect Black Body radiation curve is proof that the visible sky was in causal contact with all other parts of the visible sky at some point.
But I don't understand where this problem comes from and can't find a lucid description in any of the text. At t=0, the universe was in causal contact and in thermal equilibrium. It must be a perfect Black Body at this point. At $t=\delta$, the peak temperature of space is at some finite value, and again, the radiation would give a perfect profile because there's no physics to randomly distribute the initial energy (no prime mover) of the big bang. This goes on for $t=2\delta$, $t=3\delta$, and so on.
Time passes and we eventually get a quantum fluctuations in the fields. One of the fields that can fluctuate is energy/mass. So we get a blip in the curvature because one small section has more/less mass than the average. Are the inhomogeneities that Inflation fixes caused by the fact that the scale factor is now permanently different in the more/less dense regions?