You know, Cosmology isn't my field. (Though sometimes I wonder if I should change that...)
I have been thinking about what the observational differences between the universe expanding because of actual momentum difference between ourselves and distant cosmological objects, and the universe expanding because inflation never actually stopped, just slowed to a subluminal rate?
it is the hubble telescope that provides the per se evidence of redshift. Then likewise the mathematical scheme of the entropic path to equilibrate that renders an 'expanding' universe.
There is no evidence other than some stars/galaxies share this 'redshift' of the light (wavelengths change). (but then mass in between the line of sight can also cause a redshift.) I would seek to find the material evidence that uses coordinates between others stars, then i believe the 'expansion' can be reduced to belief) (my prediction)
There is no dark matter/energy. As them bodies are associating between each other (exchanging energy) and that potential is not observed in any cosmology that i know of. ie....think in casimir in which 2 bodies can increase a potential by exchanging energy (an entanglement caused by em)
I see there are some papers on extended inflation, some posit a model that would be predicted to make distortions in the CMB that we do not observe, but some also would produce no such artifacts.
the CMB itself could be many other fields that can be detected and have nothing to do with the big bang.
A method of proving the big bang from a central point is wrong within an entropic frame of mathematics, is if you tap a pond at a central point, then the waves do not return, unless they hit something. With newtons law of motion that would mean, nothing is affecting the mass if existence was in a vacuum; the mass would maintain its trjectory, indefinitely. (no mass would return to combine into stars).
These points of logic can assist any in observing from their own perspective.
And I am trying to figure out what experiment would show us if space were still inflating?
The answer to that is found by noting that the foolishness held to the idea of 'entropy' as conditioned in the 2nd law of thermodynamics created the foundations to a REQUIREMENT of an expanding universe. Otherwise, i rather enjoy your inquiry.
Try another idea; if the universe is expanding and the per se particles can release in a vector, then the stars on the outer edge would be releasing a solar wind, away from the center of the universe, hence a per se 'expansion' either exists, or i have the concept that energy could not go out to a nothing, and that SHOULD be provable.
ie... since there is no perfect vacuum anywhere between 2 points of mass, then that idea would be tough to prove.
But it is one that I am working on and so far, the one item that renders the concept to a logical frame is the blackness of space. (ie.... there is nothing there to detect, without a detector (mass) then the exchange is relevant to the recieving mass (double slit experiment, shares the mass of the detector, IS relevant)
There, you now have my speculations too!