@Mordred No. I want you to take your own plot of the scale factor as a function of time and paste it. I will mark a points on its curve and you will tell me the values of the redshift in these points. How about that?

Already provided a dataset use that it incorporates the full FLRW metric with the relations I described previously and used the Lineweaver and Davies paper for its benchmark tests.

 

@Mordred What is more understandable for the human brain - your table or a simple plot?

If you cannot get a specific value at a specific point on any graph does it matter ?

Edited July 19, 20241 yr by Mordred

@Mordred can you say where a=0 and a=1 are?

yes but you can get that answer directly from the calculator in my link including any associated graphs

https://light-cone-calc.github.io/

its quite versatile but doesn't port the graphs well even getting the latex here on this site requires altering the latex commands.

You can arbitrarily set any cosmological parameters you choose to use.

@Mordred is the redshift 0 or infinite for a=0?

You do understand that the scale factor is a dimensionless constant do you not understand how that constant is defined ?

ask yourself what calculation allows the scale factor to become dimensionless and ask yourself once again the question you just posed.

@Mordred redshift is dimensionless as well as the scale factor, what's the problem?

Are you sure that the scale factor is constant?

Edited July 20, 20241 yr by Nicram

how many times have I stated above including the mathematics that its not constant The term constant of proportionality simply describes a dimensionless scalar value.

look directly at the following relation

\[\frac{a}{a_0}\] where

\(a_0\) is scale factor today now answer your own question what would happen if you place a zero in the denominator ?

Edited July 20, 20241 yr by Mordred

Listen, I am interested in a relation between a/a0 and z, ok? a0 = 1 and I am not going to mess with it. I am messing with a, because its a variable.

What's the value of z for a/a0 = 1?

If your discussing cosmological redshift YOU MUST include the scale factor a and understand how it works. Especially when it comes to how cosmological redshift defines Z mathematically

Once again I can prove that using GR but that would likely be a waste of time

4 minutes ago, Nicram said:

Listen, I am interested in a relation between a/a0 and z, ok? a0 = 1 and I am not going to mess with it. I am messing with a, because its a variable.

What's the value of z for a/a0 = 1?

1

give you a clue

the radius of a describes today is the size of the observable universe today if the size of the universe then you have no cosmological redshift

Edited July 20, 20241 yr by Mordred

Is the value of z > 0 for a/a0 < 1 ?

@Mordred you've just changed zero to 1 for a/a0 = 1

If z = 1 for a/a0=1, what about the equation z+1 = a0/a ?

Edited July 20, 20241 yr by Nicram

\[a=\frac{R}{R_o}\] set radius now as 1

(\(R_0=1\) if the radius in the numerator is the same the by simple division the answer is 1

1/1=1.  Value of Z is zero...

Edited July 20, 20241 yr by Mordred

If z = 1 for a/a0=1, what about the equation z+1 = a0/a ?

I'm asking again. What's the value of z for a/a0 = 1 ?

Edited July 20, 20241 yr by Nicram

your comparing two radius relations I already provided the answer.

\(R_0=1\)\ and \(a_0=1\) when the universe is half our size you will get the answer 0.5

@Mordred You've just told me that half if equal to 0.5, are you aware of that?

wow just wow

1/2=0.5=50%

radius now=1

radius at previous or time yet to come is the numerator same with the scale factor. If radius of the universe is half the radius as it is now a=0.5 from observer now

\[{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&Scale (a)&S&T (Gyr)&D_{then}(Gly) \\ \hline 1.10e+3&9.08e-4&1.10e+3&3.66e-4&4.11e-2\\ \hline 5.46e+2&1.83e-3&5.47e+2&1.16e-3&8.18e-2\\ \hline 2.70e+2&3.69e-3&2.71e+2&3.55e-3&1.61e-1\\ \hline 1.34e+2&7.43e-3&1.35e+2&1.06e-2&3.16e-1\\ \hline 6.58e+1&1.50e-2&6.68e+1&3.08e-2&6.09e-1\\ \hline 3.22e+1&3.01e-2&3.32e+1&8.92e-2&1.15e+0\\ \hline 1.55e+1&6.07e-2&1.65e+1&2.57e-1&2.08e+0\\ \hline 7.18e+0&1.22e-1&8.18e+0&7.36e-1&3.54e+0\\ \hline 3.06e+0&2.46e-1&4.06e+0&2.10e+0&5.27e+0\\ \hline 1.01e+0&4.96e-1&2.01e+0&5.79e+0&5.56e+0\\ \hline 0.00e+0&1.00e+0&1.00e+0&1.38e+1&0.00e+0\\ \hline \end{array}}\]

 

 

universe now on this graph is a=1 bottom row

 value of a at z=1100 top row is top row

 

Edited July 20, 20241 yr by Mordred

Top row: z = 1100, a = 0.001
Bottom row: z = 0, a = 1
Do you confirm?

look at my top row \[a= 9.08\times 10^-4\] its right there on top

@Mordred have you heard about rounding?

Do you confirm?

Edited July 20, 20241 yr by Nicram

of course but if I already provide the answer can you understand my response now 

do you confirm

I confirm.

In our universe a is increasing. Is z increasing with a or decreasing with a in our universe?

Lets put it simply the one doing the Observing the scale factor and his observable universe radius is always =1

so the denominator is always set at 1

event being observed is always the numerator and your comparing the radius of the universe of the observer to the radius of the event.

If you had some past observer his value will be 1 as he is the one observing and still the denominator the event remains as the numerator on top that observer is measuring

Will a/a0 be ever > 1 ?