Okay, I know it sounds weird, but hear me out:
We know space is expanding, sure. That's been established science for a while now. All three spatial dimensions at the same (increasing) rate.
So ... why should we assume that the 4th dimension -- time -- is static and unchanging like we used to think space was? Could time also be expanding or contracting? (Expanding seems more likely, as it would match what the other dimensions are doing.) After all, spacetime is all one thing, really. Space and time are inextricably linked. When you think of it that way, it seems nearly impossible that space would be expanding while time is not. Spacetime is expanding, so wouldn't that include time as well?
My question here is: what would it look like, subjectively, from our perspective inside it, if time was expanding just like space? Would we be able to measure it at all? Would there be any difference? Could the acceleration of space expansion ('dark energy') actually be explained by time expansion instead?
For a moment, imagine a universe where time definitely is expanding. Even if you don't think time could really be expanding, let's think about that hypothetical universe where it definitely is. What would that universe be like? How would it be different -- if at all -- from our universe?
Does it even matter? If time is expanding, but we still experience it passing at a constant rate, why would we even care whether it's expanding or not? An observer somehow watching it happen from 'outside of time' might, say, see things happening slower and slower ... but for beings living inside of spacetime, with their subjective perceptions also dependent upon the flow of time, would it actually change anything at all?
I beleive time is expanding as with space, the present is the boundry of the universe, the perimeter of but one dimension of its shape, the past is set within the body of the shape, but the future is yet to exist, it has not yet been expanded into
As for how we would perceive times expansion speeding or slowing, i dont think we can, but maybe we could infer it like counting tree rings, but ive no clue
I'll caution that my above is from my imagination not any citable journal article or experiment
An interesting thought ... and perhaps it could even explain the accelerating expansion of space? Not sure if I'm approaching the idea the same way as you are, but it's giving me ideas.
Suppose time is a sphere, with the interior representing the past, the exterior representing the future, and the surface representing 'now'. All three spatial dimensions are mapped to the surface of this time sphere. As the sphere expanded from past into future, the surface area of the sphere would increase. But not just increase at a steady rate! Let's assume the 'radius of time' does increase at a steady rate from past to future. And then look at the relation of sphere radius (purple line) to sphere surface area (blue line):
When the radius is increased at a steady rate, the surface area increases at an accelerating rate. Objects on the surface of that sphere would be accelerating away from each other in all directions (just like we observe).
Viewing time as an expanding sphere and (contemporary) space as the surface of that sphere could potentially explain both the expansion of the universe and the 'dark energy' acceleration of that expansion.
(Though it does seem like something that would be very untestabable, unfalsifiable, and not particularly useful for making novel predictions.)