Nicram

@Mordred I didn't need to plot the scale's factor function myself, so I didn't need these details. @Mordred am I wrong, or have you still not opened my last picture?

@Mordred it's sufficient to know that it changes over time, that it grows, and where are its starting and ending points

@Mordred What good did it do in context of the integral, that just needs FLRW metric, that is the trivial general metric with the inserted scale factor from Friedmann equations? What good did it do to explain all the details of parametric form of scale factor?

@swansont Everyone is subject to the same dynamic, do yes, it’s fair. It means that this dynamics is equally unfair to everyone. while Mordred is taking the time to post actual material, including a lot of math. Would you really try to teach someone the principles like him, with the avalanche of not so simple maths? Would you throw this avalanche after allegedly knowing the problem, that is introduced, or would you really try to understand the problem, before you give your explanation? including a lot of math. Have you heard about Copy Paste? sense of entitlement, that you don’t have to put in the same effort I didn't have my content in this forum's format to do the same. I admit, that I didn't respect your rules. I'm sorry for that. even though you own the burden of proof here Would you admit that proof in a different format is not less valid? @Mordred I apologised you for this accusation. I apologise again.

I hope this time you will open it and read it. They were already mixed on the Velocity vs Redshift plot. The reason is that our current intergalactic space is flat or close to flat, and you have no right to integrate FLWR metric to calculate the distance. In this image I'm extensively explaining why. Christoffel symbols - Christ Awful Symbols - Love them. Do you seriously think that their downvoting without giving a reason is fair to me?

@Mordred You will also get the wrong answers, if you place yourself at the wrong point on both plots and assume proportionality of values, that are inversely proportional. I would say that's just a tiny bit more fundamental. My dear downvoters, why don't you join the discussion and tell something on topic?

@Mordred Polite you say. In your politeness, you glanced condescendingly and threw your equations avalanche at me. My dear downvoters, why don't you join the discussion and tell something on topic?

@Mordred if you don't cross out redshift values as I did and replace them with the ones I did https://i.sstatic.net/EDJB3rCZ.png You will have a striking inconsistency in term of the redshift and the scale factor values https://i.sstatic.net/7JVt6ZeK.png You know their relation. Values on the plots clearly contradict this relation.

In that case I'm sorry, but only for this accusation. Not reading what I gave you, what was a very precise strike at the fundamentals of the most important integral in cosmology - that's unforgivable. I'm using this reply to share something regarding downvotes anyway: https://astronomy.meta.stackexchange.com/questions/961/ Still, the question remains the same @Mordred did you figure out a way to fix the inconsistency, or will I get your usual menu again?

@Mordred I call it the downvote out of a personal grudge. Why not downvoting all of my replies now, to show a truly scientific attitude.

@Mordred You didn't.

@Mordred Our misunderstanding is epic. Where is the spacetime that stores the former values of the scale factor, so you can add their reciprocals using integration to build a distance in this way? Did you open my second picture and read the text?

@Mordred These equation are perfectly correct, until you start to integrate the scale factor (its inverse to be precise) and I've explained why in the second picture with lots and lots of text using all my powers. Where are the former values of the scale factor stored, because you need them to perform the integration.

Sorry, but where is expansion history stored, so you can build your universe from the different parts of its history? Nice to agree with you for the first time.

@Mordred This is the biggest avalanche of equations that has ever hit me I must be extremely brave or stupid for not running away from it. My mental powers are too small and lifespan too short to address all the aspects of Friedmann equations used in ΛCDM. However, I hope I can deal with the crucial one, that combines the recession velocity, Hubble parameter and a large distance. Seems like Hubble's Law. My reply is in the attached pictures. Aside from that, how do we know for sure, that dz/dt is increasing slower (maybe also with the decreasing second derivative?) than z+1? Do observations confirm it? Aside from that, did you figure out how to fix the inconsistency? Love it ❣️

Doesn't it make the spacetime flat? Because GR solution for FLRW is used to describe it, and also your description is a description of flat space-time. I can't quote you anymore using the Quote button, so I'll use italics. The rest of your post can readily be shown erroneous by simply knowing that due to expansion the recessive velocity can be greater than c. That occurs beyond the Hubble horizon. In point of detail at z=1100 the recessive velocity is 2.3 c. That's a statement based on assumption that superluminal velocities are correct. It's like saying, that I can't be correct, because I'm wrong, but without an explanation. I'm showing that these velocities are incorrect. So your graphs are in error as they do not show this detail. - same thing. Due to the equations of state the rate of expansion is also not consistent the Hubble parameter decreases in time even though expansion described by recessive velocity is accelerating. I'm not sure I can see this inconsistency, because I haven't changed the shape of the curves. Does the increasing Hubble constant is the effect of changing the time direction by me? Also, is decreasing Hubble constant proved by observations? Please, try to correct the inconsistency I'm showing in a different way. I can't post anymore today. I've reached the maximum number of posts I can make per day.

These are on astronomy stackexchange. My request to you - If I'm wrong, try to correct the inconsistency I'm showing in a different way.

Please, try to correct the inconsistency I'm showing in a different way. And yet it is.

The first mistake you make is thinking that spacetime is curved along the scale factor's time axis. The most fundamental description of spacetime is given by the metric tensor. For the current intergalactic space it has completely different values from the one that was describing the early, dense-energy universe. Physical link between the former tensor and the present one does not exist. There is no time curvature across the universe history, because the past is completely gone with the former values of the metric tensor. Spacetime in its form described by the tensor exists only for the time of its metric. That's my point of view and also the reason why the changing rate of expansion, given by a'(t)/a(t) is not causing the curvature of spacetime. That's also the reason why we can compare GR and SR (velocity vs redshift as well as scale f. vs time) on the same plot. That's because a single point on GR curve (ΛCDM) represents the inertial snapshot of the universe. If we're considering only snapshots, that are the single points on the curves, these velocities are equal up to now. Curves are made of these points, so these velocities are always equal (up to now). This makes cosmological redshift and Doppler redshift equal. I'm begging you to make an exception this time. I'm already mentally exhausted by proving Doppler's accuracy for CMB redshift and recession velocity.

https://astronomy.stackexchange.com/questions/58066/