The Doppler effect doesn't have to be linear; consider acceleration. Can you post the link to the quoted reference? I'd like to see it in context.
Sure, but you should already know it....
Hubble's law - Wikipedia
Understand:
“The "redshift velocity" vrs is not so simply related to real velocity at larger velocities, however, and this terminology leads to confusion if interpreted as a real velocity.”
So even if they use the terms velocity, they are not talking about a real velocity.... hence your confusion, it has led you into thinking it is a real velocity they are discussing, when in fact they are discussing scale changes....
Also understand:
“According to this approach, the relation cz = vr is an approximation valid at low redshifts, to be replaced by a relation at large redshifts that is model-dependent......
.....Strictly speaking, neither v nor D in the formula are directly observable, because they are properties nowof a galaxy, whereas our observations refer to the galaxy in the past, at the time that the light we currently see left it........
.......For distant galaxies, v (or D) cannot be calculated from z without specifying a detailed model for how H changes with time. The redshift is not even directly related to the recession velocity at the time the light set out, but it does have a simple interpretation: (1+z)is the factor by which the universe has expanded while the photon was travelling towards the observer.”
It is not the recessional velocity the redshift is related to, but the changing scale of space based upon the model used.
And just like our argument about time, the Hubble constant has a changing value in the past. It is no more constant than time is, they just refuse to adjust for time dilation because it would upset their age calculations.
“The parameter
is commonly called the “Hubble constant”, but that is a misnomer since it is constant in space only at a fixed time; it varies with time in nearly all cosmological models, and all observations of far distant objects are also observations into the distant past, when the “constant” had a different value.”
And any value you calculate into the past will be incorrect, because time was varying with the acceleration of the universe as well, but is not accounted for..... and why? Because that would require actually changing every model in existence to match the reality of time dilation.....
And you don’t even want to get into its derivation and exponential adjustment for dark energy which requires using Einstein’s cosmological constant which is claimed to be the biggest mistake of his life.......
I understand their term velocity confuses most into thinking they are talking of a real velocity. But they are not, but the changing scale factor of space. So we are not discussing Doppler shifts which require real velocities, nor can Hubble’s law actually be used, since it requires real velocities as well. They have fooled you with a bait and switch, and you are simply parroting what you were taught. Understandable, but not supportable.
Hence Hubble’s stand: “Hubble believed that his count data gave a more reasonable result concerning spatial curvature if the redshift correction was made assuming no recession. To the very end of his writings he maintained this position, favouring (or at the very least keeping open) the model where no true expansion exists, and therefore that the redshift "represents a hitherto unrecognized principle of nature.”
Even Hubble understood the velocity was not a real velocity, only apparent, and that no “continuing accelerating” expansion existed....
Accept the reality, not the fantasy of accelerating expansion.
A New Non-Doppler Redshift