How can you tell the age of such a universe without assuming the world line of the material observer? How would you calculate it?
SI definition of a second: "The duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom." If we give the cosmic time (equal to the universe age equal to the proper time of the observer resting in the CMB reference frame) in seconds, we can easily give it in the number of radiation periods from SI definition of a second.
In the same manner we can define a physical, conformal age of the universe. That's the duration of a certain number of the extending CMB radiation periods proportional to the extending peak wavelength of this radiation that passed through a point at which the CMB is isotropic, since its emission. Proportionality factor is the speed of light, because c=λ/T where λ is the extending peak wavelength, and T is the extending wave period.
Conformal time η=∫dη=∫dt/a(t)=47Gy is the conformal age of the universe and I don't question it. I'm proposing a physical definition for it. The inverse of the scale factor 1/a(t) is increasing with time counted backwards, because 0<a(t)≤1 and a(t₀)=1, where t₀ is the present, proper age of the universe. That makes dt/a(t)=(z(t)+1)dt the equivalent of the wave period extending over time counted backwards. We're integrating over it to sum it up. The observed redshift z(t) of light emitted at the past time t and increased by 1 is equal to the expansion of the wavelength, period and the universe itself.
Is there something wrong with the proposed, physical definition?
Astronomy has been calling it non-physical, coordinate time since forever. I'm calling it physical and giving the explanation. If it's correct, then the universe may actually be 47 (not 13.8) billion years old, corresponding to 47 billion light years of the observable universe radius.
Answering the title question: The universe itself would be aging - conformally, along with the decreasing energy density and temperature of the background radiation.
Astronomy is in Crisis... And it's incredibly exciting - Kurzgesagt - https://www.youtube.com/watch?v=zozEm4f_dlw
In summary: 1. Dark matter distribution doesn’t exactly fit the galaxy rotation curves. 2. Dark energy doesn't exactly fit the expansion. There are serious premises of a non-accelerating expansion based on "strong progenitor age bias in supernovae". 3. Hubble tension remains a persistent and unsolvable mismatch between the expansion rates. 4. There are so old galaxies observed in such a young universe, that ΛCDM model simply doesn’t allow them. 5. These galaxies can have from 1% to 100% contribution to the CMB radiation. How funny is that? 6. The excess radio dipole doesn't match our peculiar velocity calculated from the CMB dipole. Plenty of things simply don't add up.
We are just assuming based on the limited observation we have made. Physics, specially the astrophysics could be much more different that what we think now. And there's lot more we can't observe so maybe would never know all of it ever.
Do we have any such reason to believe the laws of physics aren’t universal?
Our physics is model based not absolute truth. We see and would be able to see just a small part of the universe which may not be sufficient to explain all the physical forces and nature of the whole universe.
We may predict but might never be able to fully explain physics.
Ok, so, no. Of course physics is a model. These topics are a good thought experiment but shouldn’t be held in equal regard as the models we have crafted
At the same time, nor should one think of the current working models as reality's truth. They are limited and their scope is bound to what we can observe and make sense of, which could be very far from reality itself.
No one is claiming that, we’re discussing observations within our observable universe.
If you go out past the observable universe it’s like the Farlands in Minecraft, the terrain generation gets really glitchy.
Photons would be red shifting as the universe expanded, but without matter to generate photons, there would be no CMB. I'm not sure what you would see.
Is there dark matter in this hypothetical universe?
No dark matter.
In my understanding, the background radiation was already there before and up to recombination, when the hydrogen atoms were created, and some of it was absorbed by them in the process of their creation. However, the electrons in newly formed atoms were generally in the excited state from which they immediately transitioned to the ground state, emitting the photons that were added back to the background radiation. Is this incorrect?