In an inflationary (or anti inflationary,I suppose) universe are there spacetime curvature effects leading to different time/space measurements wrt two different reference frames?

I understand that the universe is apparently flat in terms of curvature but does its agreed expansion mean that measurements need to be adjusted to account for it?

yes changes to the scale factor evolution is non linear over the Universes history this leads to numerous adjustments that must be made to linear relations (first order formulas) where second order relations must be incorperated example of second order being acceleration example accelerating expansion.

various measurements as a result of the above non linear expansion rates that require corrections is angular diameter size, angular diameter distance, look back time (ie age of universe at a given distance usually as a function of redshift), redshift corrections, luminosity distance corrections.

the above corrections must apply the equations of state for matter, radiation, Lambda and any applicable curvature term.

for example if one tried to take the time dilation formula under SR once you get to recessive velocity greater than c then that equation will give wrong answers. I know your not strong in the mathematics but If your interested in the corrections for higher recessive velocities they are here

corrections to look back time

I would have to dig up the corrections for angular diameter distance , luminosity distance etc but the previous two examples show how the equations of state are involved. There are also other factors such as the relation between angular size and angular distance. One counter intuitive example is that above redshift 1.5 Z approximately the angular size increases rather that decreases.

32 minutes ago, Mordred said:

yes changes to the scale factor evolution is non linear over the Universes history this leads to numerous adjustments that must be made to linear relations (first order formulas) where second order relations must be incorperated example of second order being acceleration example accelerating expansion.

various measurements as a result of the above non linear expansion rates that require corrections is angular diameter size, angular diameter distance, look back time (ie age of universe at a given distance usually as a function of redshift), redshift corrections, luminosity distance corrections.

the above corrections must apply the equations of state for matter, radiation, Lambda and any applicable curvature term.

for example if one tried to take the time dilation formula under SR once you get to recessive velocity greater than c then that equation will give wrong answers. I know your not strong in the mathematics but If your interested in the corrections for higher recessive velocities they are here

corrections to look back time

I would have to dig up the corrections for angular diameter distance , luminosity distance etc but the previous two examples show how the equations of state are involved. There are also other factors such as the relation between angular size and angular distance. One counter intuitive example is that above redshift 1.5 Z approximately the angular size increases rather that decreases.

It seems (crudely)from the beginning of your linked post that the formulae employed may be based on the normal spacetime metric with extra input from the rate of expansion?

Do the faster than c recessionary speeds that are now in play have their counterparts in the earliest epochs in the universe?

For example, the inflationary period occurred, if I am correct some short time after T+10^-43 seconds.Were there superluminal recessionary speeds during that epoch also?

From the incredible rate of inflation then it would seem possible to me but perhaps the actual highest speed of recession remained below c despite the more than ferocious accelerated rate of the inflation?

28 minutes ago, geordief said:

Do the faster than c recessionary speeds that are now in play have their counterparts in the earliest epochs in the universe?

It should be noted that expansion has units of inverse time, not speed, although it is usually expressed as speed per distance. For a flat (three-dimensional) universe described by the FLRW metric, the recession speed at a particular time is directly proportional to the distance, and therefore there will always be some distance beyond which is receding faster than c. However, it should be noted that when we look outward, we are looking at the past, so the observed recession speed is not necessarily proportional to the observed distance.

Yes there is superluminal expansion during inflation however the period during such time would be more problematic as the mean free path of photons would be too short to receive signals from emitter to observer aka the dark ages. Mean free path time estimate 10^{-32} seconds.

So you wouldn't be able to recieve signals between two inertial frames of reference

25 minutes ago, KJW said:

It should be noted that expansion has units of inverse time, not speed, although it is usually expressed as speed per distance. For a flat (three-dimensional) universe described by the FLRW metric, the recession speed at a particular time is directly proportional to the distance, and therefore there will always be some distance beyond which is receding faster than c. However, it should be noted that when we look outward, we are looking at the past, so the observed recession speed is not necessarily proportional to the observed distance.

Good point

Time always passes at the same rate in everyone's own frame.

However the very fact that expansion increases the time base of an emitted light signal, resulting in red shift or a 'stretching' of the signal's wavelength,, means that relational time between distant events will vary.
this effect is not due to gravitational effects because, as you say, global curvature is very nearly flat.

1 hour ago, MigL said:

this effect is not due to gravitational effects

But metric expansion is a gravitational effect…?

1 hour ago, MigL said:

because, as you say, global curvature is very nearly flat.

That’s purely spatial curvature though. The Riemann tensor as a whole does not vanish in FLRW spacetime, even for the case k=0.

I found after some digging a useful article showing some of the corrections mentioned earlier for higher redshift distances

https://people.ast.cam.ac.uk/~pettini/Intro%20Cosmology/Lecture05.pdf

One thing I should mention often textbooks etc on a topic gives you the first order formulas for various things like redshift, luminosity distance, angular diameter distance etc.

You rarely find the more advanced formulas in common literature. Those formulas tend to be something that the instructor will have you derive yourself. The above lecture lesson is an example

38 minutes ago, Markus Hanke said:

But metric expansion is a gravitational effect…?

That’s purely spatial curvature though. The Riemann tensor as a whole does not vanish in FLRW spacetime, even for the case k=0.

We have to be careful here K is a specific relationship with the critical density formula. When K=0 precisely then the energy mass density equals the critical density. If K=1 then this describes a closed universe where the energy density is greater than the critical density. If K=-1 then the mass energy density is less than critical density.( open universe). Though open closed universes are an older application of the critical density formula.

With regards to inflation one of the problems inflation addresses is the fatness problem related to the above. K value remains unchanging throughout the universes expansionary history.

For example if in the first case k is precisely zero the universe is static neither expanding nor contracting.

Edited January 19Jan 19 by Mordred

On 1/19/2026 at 5:53 AM, Mordred said:

For example if in the first case k is precisely zero the universe is static neither expanding nor contracting.

I don’t think this is correct. k=0 just means that the universe is spatially flat, but that doesn’t imply that a(t) must necessarily be unity. You can have a spatially flat, metrically expanding/contracting universe.

But in either case, the Riemann tensor does not vanish, irrespective of the value of k.

Agreed it's not perfectly flat with regards to the Rheimann tensor as to the earlier statement I made

"where (tS ) is the scale factor and k is a constant which denotes the spatial curvature of the three-space and could be normalized to the values +1, 0, –1. When k = 0 the three-space is flat and the model is called Einstein de-Sitter static model, when k = +1 and k = –1 the three-space are of positive and negative constant curvature; these incorporate the closed and open Friedmann models respectively."

note the statement 3 space which also agrees with your earlier statement.

https://mpra.ub.uni-muenchen.de/52402/1/MPRA_paper_52402.pdf

Obviously we're both aware a static solution is considered impossible. The other use for the critical density formula as shown above ties into the fate of the universe.

Edited January 20Jan 20 by Mordred