Yea, I suppose it may be better to say that LCDM modeling is solid, but its original hot, dense, low entropy origin is not, due to many competing models.
I have searched the forum a bit but could not find a discussion of this Astrophysics letter:
'Evidence for anisotropy of cosmic acceleration', Jacques Colin et. al, 18 Oct 2019.
Can someone please direct me to any forum discussion?
It could be read both ways around, so I tried to answer this part of the OP question, where he asked about the scale factors from a given time interval.
For large scales I think we are still using the 2018 Planck Collaboration data set, with ##H_0=67.4## +- 0.5 km/s/Mpc. One must remember that the whole dataset as a unit is consistent with the LCDM model and one cannot just change one parameter, like ##H_0##, without changing at least some of...
Hmmm, OK, but I thought that the OP's concern was that if you only have a light travel time and two scale factors, how do you find one of the mentioned proper distances.
The only practical way I can think of is to make Earth the receiving galaxy and then find out what the scale factor (or...
In terms of the OP question, as I understood it, I think yes. Light does not travel the proper distance in expanding space, but simply ##c\Delta t##. By the time it arrives at the receiver, the proper distance between emitter and receiver is larger than the distance light actually traveled.
Excellent piece of writing by Brian - here is the Insights link:
https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/
Looking at the graph of ##a## vs ##t##, what you said is actually roughly true for a large chunk of cosmic time!
It is not true for the first 3 Giga years or so due to dominant radiation energy. Also not for the last 4 Gy due to the accelerated expansion, but still close.
It requires a bit of...
In a cosmos with radiation, matter and a cosmological constant (like ours), it is not straightforward to find the expansion factor change from a cosmological time interval, except approximately (if the latter is small and the expansion close to linear over time).
As you expected, the general...
Nope, FLRW is a spacetime metric, because H has time in it: ##H = \frac{\dot {a}}{a}##.
You must distinguish between curved space and curved spacetime. Minkowski spacetime is flat, because it does not expand: ##\kappa=0## refers to zero spatial curvature, but you must also have ##\dot {a} =...
Without going into the technical stuff, as I understand it, a Milne universe is spatially flat, but has negative spacetime curvature, because the (empty) space is expanding at a constant rate (##\ddot a = 0)##.
I think the Op's interest is not velocity time dilation, but rather converting the (static) gravitational time dilation at a distance r from a large prime mass, to the actual mass of the prime. It is easily coming out of
$$d\tau/dt = \sqrt{1-2M/r}$$
provided that ##d\tau/dt## is known, but how...
Peter has given you enough info in #4 above to do what you have asked - check again.
But this is a very round-about way for obtaining the mass of an astronomical object. Normally one would simply observe the period and eccentricity of any object orbiting the prime mass from some distance...