# How can cosmic inflation make an infinite universe homogeneous?

As it is explained in this video, one of cosmic inflation's observable effects is the homogeneity of our universe. Inflation allows two points on the different sides of the observable universe to be causally connected at some point in time, so they may exchange their mass densities and temperatures, which are then going to be about the same for both of them.

While I do understand, that this effect doesn't have to end on the edge of the observable universe and might go on for whatever distance the rate of inflation will make it to, I do not understand how this could be valid for the entire Universe if it is infinite. From my guessing, if the Universe is infinite, there will allways be two points, that was never causally connected, no matter how fast it expanded at the inflation period. That will mean, that, while the Universe should be homogeneous on the sufficiently large scales, it doesn't have to on the scales even larger.

I guess I either don't fully understand the idea of cosmic inflation or don't get the particular way the Universe is infinite in.

• AFAIK Inflation explains why the observable universe is very homogeneous. Not the entire universe. – Rob Jeffries Mar 30 '16 at 8:39
• @RobJeffries nails it. – pela Mar 30 '16 at 9:07
• @RobJeffries, but then it means that cosmological principle is not applicable to the entire Universe. Is it OK? And, as I understand, it is still theoretically possible to find some kind of gradient in the observable universe's matter distribution, as it should be the case, that some of its parts were previously causally connected to a region of space other parts were never connected to. – harry Mar 30 '16 at 10:16

Without inflation, we can do the following crude calculation. The cosmic microwave background was formed about 300,000 years after the big bang, at a redshift of about 1100. Thus causally connected regions at the epoch of CMB formation would have a radius of $\sim 300,000$ light years, which has now expanded by a factor of 1100 to be $3.3\times 10^{8}$ light years in radius.
This can be compared with the radius of the observable universe, which is currently around 46 billion light years. This means that causally connected regions should only be $\sim 4 \times 10^{-7}$ of the observable universe, or equivalently, patches of CMB of $\sim 2$ degrees radius on the sky are causally connected. This is clearly not the case as the variations in the CMB are no more than about 1 part in $10^{5}$ across the whole sky.