Do me a favor, forget about 47 and 13.8 billion years in case of a universe without matter, and answer my question. What would be aging and how?

Edited December 29, 2025Dec 29 by Jacek

oh gee all physical processes such as temperature change can be related to age. Age is not strictly a factor of matter only. it is a duration of events. the evolutionary history of our universe can be segmented using age. Nuclear decay is simply one type of aging

Oh gee, like I didn't write that the universe itself would be aging along with the decreasing energy density and temperature of its radiation. It seems that we can agree about it. Now the question is How would you calculate its age?

Edited December 29, 2025Dec 29 by Jacek

sigh obviously were going to use the evolutionary history of our universe over time which I already know your using for your conformal distance to time relations. ie the radius of the observable universe in this case. Which is preciseley my point to my previous statements. The temperature will vary with the scale factor. Your formula you provided specified that above.

Now back to my question which you evidently don't want to answer. If you removed matter your evolutionary history of the rate the scale factor will change..... so why would you use that as a benchmark for age of the universe with a non linear curvature to the scale factors evolution through time given varying rates of expansion.

I don't want to use a scale factor of the expanding universe without matter. I'm using the scale factor from the Friedmann equations with all our density parameters. You're talking about varying expansion rates and I'm repeating that expansion rate is totally based on the scale factor and its time derivative.

Answering your problematic question: Conformal time is better for the universe because universe is mostly spacetime filled with radiation in terms of its volume. In terms of energy contribution the radiation is negligible, but it expands along with the universe and it's filling it.

Edited December 29, 2025Dec 29 by Jacek

Radiation is not the driving force to expansion today that is the cosmological constant. Our universe underwent 3 distinct era... radiation dominant, matter dominant and today matter dominant.

I hope you realize that conformal time specifies the use of commoving distance and not proper distance if not see the first 2 graphs here

https://arxiv.org/abs/astro-ph/0310808

Nothing I wrote contradicts your statements.

edit forgot to add why not just use radiation also pertains to angular diameter distance. You need to account for all influences when it comes to distance measurements.

I use a(t) calculated from the Friedmann equations with all the contributions, and I use it in the conformal time calculation ∫dt/a(t)=-∫dz/H(z), so all the history of expansion with its changing rate is factored in.

Tell you what take equation 14 and apply it to equation 30

https://arxiv.org/pdf/astro-ph/9905116

this is your graph here

https://ned.ipac.caltech.edu/level5/Hogg/Hogg10.html

then look at the difference using proper distance vs commoving distance

each has its use but look back time is how you determine the age of the universe see first link for equation and relations with an multicomponent universe like our own. That should answer why you need all components contributing to expansion >particularly when it comes to angular diameter distance etc.

What is incomprehensible for you in my previous comment, where I state, that I use all the contributions in the Friedmann equations? How many times are you going to repeat that I need all of them?

when you realize that the radius of the universe given by Google is the proper distance and not the commoving distance which is required by conformal time which would not be 47 Gyrs

edit sorry other way around the point you should be seeing is commoving time is distinct from proper time when it comes to SR and GR treatments. Conformal distance is a rescaling in that regard. Your opening post argued that proper distance is preferred over commoving distances but obviously you didn't look at those 2 formulas and determined which is being applied did you ?

Edited December 29, 2025Dec 29 by Mordred

But conformal time of our universe is 47 Gy and it directly corresponds to the proper distance 47 GLy. You just multiply this conformal time by c to get the proper distance.

only in a spatially flat universe not a curved. see above you missed my edit

No, I didn't miss your edit. You made it after my comment.

I live in spatially flat universe assuming large scale homogeneity. You don't?

cosmology like to allow for all 3 possibilities hence its versatility and you still missed that we already use conformal distance to calculate the age of the universe. equation 14 and 30....

hence cosmic time is not the same as proper time

Edited December 29, 2025Dec 29 by Mordred

Yes it is, in spatially flat universe. I restrict myself to it and leave you with all the versatility.

No it's not do you want the proper time corrections beyond Hubble Horizon for when the recessive velocity exceeds c ? SR without those corrections will give you the wrong answer.

Same as GR without accounting for those higher recessive velocities.

Hint proper time uses proper distance not commoving distance. Cosmological time uses commoving distance to a commoving observer. Age of the Universe is determined by the latter not the former

Edited December 29, 2025Dec 29 by Mordred

Are you saying that comoving observers separated by the distance greater than Hubble Radius and receding with v>c are not the same proper age at the same cosmic time in the spatially flat universe, assuming they've been existing since the emission of the CMB?

Are you saying that universe age is not equal to the proper age of these comoving observers, neglecting the fact that the CMB was emitted some time after the BB?

Edited December 29, 2025Dec 29 by Jacek

if you were to apply the Lorentz transformations under SR once you exceed the Hubble Horizon then the recessive velocities given by Hubble's law will exceed c. At Z=1100 for example the recessive velocity is 3.2 c. To get the corrections you have to apply the evolution densities of matter, radiation and the cosmological constant to account for beyond the Hubble horizon the the cosmological event horizon or particle horizon. The Hubble horizon is z=1.46 here is the methodology for the corrections

a couple of posts up in that thread. I also have the more accurate or modern used look back time corrections its compatible with Peeple's equation 14

Why on earth are you talking to me about the Lorentz transformation, when I'm asking you whether the age of these comoving observers is equal to the universe age?

were discussing proper age vs cosmological age. Conformal time does not describe proper time and its age is in cosmological time as per its usage in the FLRW metric equations which uses the commoving observer on a commoving coordinate system. Proper time is coordinate independent. Conformal time is not, it relies on those previously mentioned criteria.

That should answer your last question as I did mention commoving observer and conformal time uses commoving coordinates. Proper time however does not and that distinction is extremely important when it comes to how GR or SR applies to the FLRW metric.

That's why my physical definition of the conformal time requires the point at which the CMB is isotropic, so you can assign its position to a comoving observer. It requires the CMB rest frame, and the fact that proper time is coordinate independent chages nothing in that matter.

Your answers are one of the most evasive in the world, @Mordred and you're very, very tiring.

Edited December 29, 2025Dec 29 by Jacek

Its because if your following what Im describing instead of delivering straight answers you might think about it.

It seems your trying to find preferred frame. You dont want that. Keep it emitter/ observer. As observer you already have a frame of reference which is already assigned by the usage of the scale factor to some other past moment provided by the redshift function.

The CMB is only 1 possible past moment and even the surface of last scatterring spans a number of years. Which arbitrary point will you choose ? Its isn't some discrete point in time.

I doubt you've worked with the Saha equations with regards to hydrogen dropping out of thermal equilibrium which traps the free electrons. For example the aforementioned 3000 kelvin mentioned this thread represents the temp where 75% of the hydrogen formation. At 4000 kelvin it's 50% etc. Its not some one point in time.

After all the static on your radio is the noise from the CMB today and not the CMB at say Z=1050 or 1100

Which time during the CMBs presence will you choose? As it's still present today as well as 13+ billion years ago ?

Keep in mind I could have stated on my first post that how the age of the Universe was determined is already using conformal time from my first post. However it was clear you were not aware of that nor aware of the distinction between conformal time vs proper time as it pertains to GR four momentum.

Edited December 29, 2025Dec 29 by Mordred

Enough is enough.

You also need your observer to rest in the CMB reference frame so that his proper time can be equal to the proper age of the universe, so you also need the CMB reference frame.

Edited December 29, 2025Dec 29 by Jacek