I've been reading about cosmic inflation recently and I feel like I owe some cosmologists an apology because it's a much more fleshed out theory than I realized. For some reason the detailed physics basically never gets talked about outside of the people who actually study it, which is a shame because it's really cool.
So the basic story as I understood it before goes like this. Light travels at a finite speed and the universe has a finite age, so at any given time there are objects in the sky we're only just receiving first light from because it's taken the full age of the universe for it to reach us. That means that when we look in opposite directions, we can see distant objects that haven't yet had time to see each other. But that's confusing between the universe seems to be very isotropic. The bulk properties like overall density and temperature and so on seem to be even in all directions, which is hard to explain for patches of sky that have never been in causal contact and so had no opportunity to thermalize. So we invoke inflation: at some early point in the universe's history, it was in a false vacuum state that gave led to a phenomenally high density of dark energy, causing the universe to expand very rapidly. That means that regions that were originally in contact got flung far apart, so while these new patches of sky we're seeing have never been causally connected in the universe's post-inflationary history, they were prior to inflation, thus explaining how they thermalized.
And I thought that's basically all there was to the proposal. Some undetermined high-energy false vacuum would resolve this so-called horizon problem and we don't really have any better explanation, so we chuck into our standard model of cosmology. But it turns out that's actually a really simplified picture. For one, the false vacuum idea is very outdated. It was originally proposed by Guth to explain some other mysteries, but it actually doesn't resolve the horizon problem at all. That kind of inflation would end when the vacuum tunnels to the current, (presumably) true vacuum state and from there nucleates a bubble of true vacuum which contains our observable universe. But that bubble would expand at the speed of light! So it's no good for allowing formerly-connected regions to recontact each other, unless we got spectacular lucky and had a large number of nucleations occur within a causal patch almost simultaneously. What we actually need is for inflation to end everywhere in the universe at almost the same time, which is where modern "slow roll" theories come from. Instead of a true false vacuum that's metastable and has to be tunneled out of, the idea is that the inflaton field sits on a verrrry gentle slope towards a cliff, at the bottom of which is our true vacuum. It slowly rolls (hence the name) down this slope semiclassically until it hits said cliff, which puts the inflationary epoch on a more-or-less consistent timer everywhere.
Theoretically, this is actually a lot less parsimonious of a theory than Guth-style inflation. Metastable vacuums are pretty ubiquitous in the theory landscape but generating a potential with just the right shape for slow roll inflation seems to require a lot more fine-tuning. But the one big advantage it has (aside from actually resolving the horizon problem, obviously) is that it makes some pretty specific observational predictions, some of which have already been confirmed way more directly than I realized! To explain why we need to be a bit more careful about the idea of cosmological horizons. The basic picture I presented before of our observable patch of universe growing as light has more time to travel gets complicated a lot by expansion. Objects are receding from us at an apparent velocity equal to their distance times the Hubble parameter H. If H were constant, which means a fully dark energy-dominated universe, objects further than c/H from us (which we say are "outside the Hubble sphere") would appear to be receding faster than c, so light they emitted would never reach us no matter how long we waited. The observable universe would stay constant in size and there would be no horizon problem.
Since our modern universe isn't entirely dark matter-dominated, H has actually been decreasing, so the picture I presented more or less works—but the inflationary universe was. Not only was there a Hubble sphere during the inflationary epoch, but it would have been unimaginably tiny, many orders of magnitude smaller than a single proton. That has a very interesting consequence: quantum fluctuations in the inflaton field with a wavelength comparable to that size are constantly getting expanded just outside of the Hubble sphere. Since those parts of the field are no longer in causal contact, they don't know that they should be oscillating anymore and the fluctuation gets "frozen" in whatever state it was in right before that happened. That frozen oscillation will then continue to expand exponentially, and since this process is happening continually during inflation you get a uniform distribution of inhomogeneities in the inflaton field at all length scales. Or rather, an almost uniform distribution. Because of the previously discussed slow roll, even during inflation H isn't exactly constant, instead decreasing very slowly. That means the Hubble sphere is growing slightly, so the quantum fluctuations getting continually frozen out have longer wavelengths and are therefore weaker (that's just a prediction that falls out of the quantum mechanics). That means that at any given time, the inhomogeneities at the largest scales have been expanding for longer, and therefore got frozen when the Hubble sphere was smaller, and so are larger in amplitude. That gives the power spectrum a slight tilt towards longer wavelengths.
The really cool thing about this is that it's measurable. We don't have direct access to the inflaton field of course, but these inhomogeneities are what produced the very slight density fluctuations in the early post-inflationary universe [1] that we observe in the CMB (and that are ultimately responsible for structure formation). And indeed, when Planck measured the power spectrum of these fluctuations, it found that it was almost flat but tilted slightly towards larger length scales. If it was exactly flat, to within the sensitivity of our observations, that would be one thing, but this subtle skew is a pretty unique prediction of slow roll inflation. There aren't many other proposals thus far that can replicate it, even ignoring the horizon problem. And that's why despite us having no real hope of observing the inflationary epoch directly, and the theoretical fine-tuning problems, and the philosophical objections of some people like Penrose, most cosmologists now consider inflation a pretty well-supported part of the standard model of cosmology.
[1]: The way fluctuations in the inflaton field produce density fluctuations post-inflation is interesting in its own right. When inflation ends, all the energy in the inflaton field gets dumped out into a bunch of Standard Model particles, so you'd think great, a slight increase in the inflaton field means more energy going into that matter hence higher density. But remember, in slow roll theories, the end of inflation always happens at the same value of the inflaton field, so all those fluctuations actually due is change when inflation ends. The matter density at the exact moment inflation ends locally is always the same, but the earlier that happens the more time there is in that region for old-fashioned post-inflationary expansion to dilute that newly formed matter before the rest of the universe catches up.















