There are lots of well understood physical processes that produce clear predictions of what we should observe if pigs were able to fly. Does that make flying pigs "well established physics"?

Here's cosmology in a nutshell for you:

You take the commonly accepted theory of gravity (precision-tested on solar system scale [1]) and assume that it works unmodified on cosmological scales, impose the "cosmological principle" (actually a maximally simplifying assumption rather than a bona fide principle) and get the FRW model [3].

The instability of FRW's static solution, the observed redshift of distant galaxies and the cosmic microwave background then lead you to the big bang, and applying (actually well-established!) nuclear physics to primordial nucleosynthesis results in good agreement with observed element abundances [4] - apart from lithium, of course [5].

But never mind that, you have bigger fish to fry, like solving the horizon [6] and flatness [7] problems which you inadvertently introduced along with the big bang.

Happily, it occurs to you (following Guth and Starobinsky) that an early period of exponential expansion would help there, and also explain the apparent absence of exotic relics from GUT symmetry breaking. GUTs are of course anything but well-established physics [8], but if high energy physicists can dream, then why can't you? Thus, inflation is born [9]. Some naysayers may claim that you have no idea what supposedly drove it, but you know better: you actually have way too many ideas. There are actually more inflationary models than any sensible person could possibly keep track of, and no way to tell which - if any - of them is correct. That's by design. Known physics can't do the job, so they must be based on hypothetical new physics capable of escaping detection in every physics experiment ever performed to date.

But never mind that, because once again, you have a more pressing problem to solve: even granting that all assumptions you've stacked up so far are correct, your model doesn't fit the data. There's just not nearly enough matter in the universe to reproduce the observed flatness, expansion history and element abundance which you just tied up so brilliantly with inflation. Then again, if you are willing to assume an undetected (and quite possibly undetectable) inflaton, why not some far more mundane, pretty much ordinary matter which just happens to be undetected (and quite possibly undetectable) too? There are even boring astronomical reasons to take the notion seriously. Crank up the density of this unknown dark matter [10] to 85% (!) of all mass in the universe, and your model works - kind of.

See, after you stuffed all that matter into your model, some enterprising astronomers went out and did their best to measure the rate at which it's causing universal expansion to slow down. Surprise: they obtain a far better fit to the data by adding a freak term to your model, Einstein's old cosmological constant [11] and making it so large (about 70% of all energy in the universe!) that it dwarfs your dark matter. Which means that according to the once-again patched model [12], the expansion is not slowing down; it's accelerating.

Oh well, you say, if I can have exponential expansion in the early universe, why not now? A flood of dark energy models follows, again more than any sensible person could possibly keep track of, again based on anything-but well established or even verifiable physics, for the same old reason: known physics can't do the job, so it must be something which eluded every physics experiment ever performed to date.

But that's still not the end of the story. Because as noted in the article linked at the top of this page, even this latest iteration produces inconsistent results when fit to two different measurements of the same quantity. So to the extent that there are "a lot of well understood physical processes that produce clear predictions about what we should observe", they are saying that the model is, in fact, wrong. Again.

[1] https://en.wikipedia.org/wiki/Tests_of_general_relativity

[2] https://en.wikipedia.org/wiki/Cosmological_principle

[3] https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr...

[4] https://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis

[5] https://en.wikipedia.org/wiki/Cosmological_lithium_problem

[6] https://en.wikipedia.org/wiki/Flatness_problem

[7] https://en.wikipedia.org/wiki/Horizon_problem

[8] https://en.wikipedia.org/wiki/Grand_Unified_Theory

[9] https://en.wikipedia.org/wiki/Inflation_(cosmology)

[10] https://en.wikipedia.org/wiki/Dark_matter

[11] https://en.wikipedia.org/wiki/Cosmological_constant

[12] https://en.wikipedia.org/wiki/Lambda-CDM_model