Inflation has made plenty of predictions that have been confirmed. The main ones are:
- The universe is almost perfectly flat. Inflation was invented to explain the flatness problem, which asks why the universe is not extremely curved. But it makes the further prediction that the universe is very very close to being flat, so close that we will never see a deviation of flatness.
- The fluctuations in the CMB are approximately gaussian. That is, if you expand the CMB's temperature fluctuations in terms of spherical harmonics, the coefficients are independent and gaussian distributed.
- The fluctuations are adiabatic, rather than isocurvature. This roughly has to do with how the temperature fluctuations impact the energy density.
- The fluctuations are almost scale invariant, but not quite, with this deviation quantified by a parameter $n_s$ called the spectral tilt which is slightly below $1$.
All of these predictions were worked out by the 80s. Around this time, cosmology had very little data. For instance, the classic cosmology textbook by Kolb and Turner (published 1994) states
To date one of the few blemishes on early universe cosmology is the lack of experimental and/or observational tests [...]. Inflation, however, is an early universe theory that is rapidly becoming amenable to test.
The main CMB precision measurement experiments were WMAP and Planck, which finished taking measurements in 2010 and 2013. (Many other experiments, all carried out after the 80s, played a role as well.) All of these four predictions have been confirmed so thoroughly that people are forgetting how recently we didn't know these things were true.
Before addressing criticisms, it should be noted that inflation is not a specific model, but a general idea, and there are many specific models that realize this idea. Criticisms of inflation generally confuse inflation with specific models of it.
The first common criticism of inflation is that many (but not all) inflation models predict eternal inflation, which leads to an infinite multiverse. One can argue that this leads to "the end of science" because the particular features of our universe (i.e. the particles and their interactions) cannot ever be predicted, but are merely randomly drawn from the multiverse. This is a valid criticism of the attitude some physicists take, but it has nothing to do with whether inflation makes valid cosmological predictions. It already has, and it was right.
The second criticism is that some inflation models don't produce the four generic predictions. That's true, but such models are universally more complicated. Kolb and Turner simply dismiss them:
Of course, theorists are a clever lot, and even these predictions are not entirely inescapable. [...] Some have even raised this to an art form, "dialing in" the terms in the potential [...] with scalar fields rolling and rebounding on their potentials like pinballs in a pinball machine! [...] When testing the inflationary paradigm it seems most fruitful to focus on the most fundamental and simplest predictions and only if they are falsified, to turn to the theorists for more exotic ideas!
While some people played with more exotic ideas, the generic predictions of all simple models turned out to be true. Inflation got it right on the first try.
