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It doesn't. First to clarify what the CMB is. It's basically just heat residuals that seem to indicate that the universe was much hotter in the past. The problem is that these heat residuals are relatively homogeneously distributed. In terms of thermdynamics this makes perfect sense - the entire temperature of an area will gradually converge, like a pot of boiling water will eventually reach room temperature.

But physically what we observe does not make any sense. Like you probably know, nothing -- including action -- can be perceived to travel faster than the speed of light. The sun is about 8 light minutes away from us. If it somehow just suddenly disappeared, we'd still see it in the sky and continue to revolve around, what would 'now' be nothing, for about 8 minutes. The observation of its disappearance and the effective causality of its disappearance (and its effect on our orbit) would happen at or very near the exact same time.

The problem with the CMB is that areas of space that should not be causally connected since light itself has not had time to go from one to the other, seem to be causally connected. In other words, with our boiling pot in a kitchen room - the eventual equilibrium that the kitchen reaches (if we assume that that entire little region is all of the space in existence) is going to vary quite substantially whether you have an e.g. 100 cubic meter kitchen or a 200 cubic meter kitchen. We should observe both sides of space acting like two independent 100 cubic meter kitchens, instead we seem them behaving like a single 200 cubic meter kitchen.

This is a major and unresolved problem that threw much of what we know out the window. It directly contradicts the big bang. To 'resolve' this, we started creating a arbitrary special conditions. Cosmic inflation is one of these. There is absolutely no reason to believe that cosmic inflation ever happened - its sole and only reason for existence is to work as a 'fix' to make what we observe fit what we thought we'd observe. This makes it illogical to use derivative things as "evidence". In particular the nature of our current CMB is in no way meaningful evidence of inflation, because inflation was hypothesized, after the fact, in no small part to fit the CMB to what we thought we'd see! In other words calling the CMB meaningful evidence of inflation is trying to provide support to a hypothesis by suggesting that the observation said hypothesis tries to explain is meaningful evidence of that hypothesis.

Any not completely idiotic hypothesis will obviously be 'evidenced' by what it tries to explain. But we have a major problem when that 'evidence' becomes all you have to rely on, and that is exactly the case here.




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