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. Mar 30, 2016 at 8:39
• @RobJeffries nails it.
– pela
Mar 30, 2016 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.
– iry
Mar 30, 2016 at 10:16

Inflation is used to explain why the observable universe is extremely homogeneous.

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.

Inflation solves this by allowing previously causally connected regions to inflate to become larger than the entire observable universe.

You appear to understand this quite well, so I am not entirely clear what your question is. We cannot know whether the entire universe is homogeneous, since we cannot measure it. The cosmological principle is an assumption that appears to hold approximately true in the observable universe, but need not apply to the universe as a whole. Indeed it is not absolutely true in the observable universe otherwise it would be quite uninteresting, containing no galaxies, clusters, or other structure. I think the only requirement on inflation is that it blows up a patch of causally connected universe so that it becomes much bigger than the observable universe at the current epoch.

• I think I just had some kind of mind barier regarding the cosmological principle's role in cosmology. It makes much more sense for it to be more like a rule of thumb, that the Universe should be homogeneous enough on the scales of the observable universe, but of course it doesn't have to be that way for any scale larger. Thank you for your answer :)
– iry
Mar 30, 2016 at 12:22
• It doesn't have to be even on the scale of the observable universe, we could look at deep space in one direction and see something very different than if we looked at deep space in the opposite direction and that wouldn't really be a problem. Inflation is our explanation for why we don't see that, that no matter where we look at the CMB it is very nearly the same. Nov 1, 2020 at 20:44