Problem interpreting Mpc/h in maps of DM

[BillSaltLake]

Problem interpreting Mpc/h in "maps" of DM

In charts of ρ distribution, such as the z = 0 image
http://www.mpa-garching.mpg.de/galform/virgo/millennium/seqF_063a_half.jpg

(taken from http://www.mpa-garching.mpg.de/galform/virgo/millennium/ ),
the distance scale is usually expressed in units of Mpc/h. In this image, there is a scale of 31.25 Mpc/h, although I think this is a misnomer-- it should be written [31.25/h] Mpc, because h is decreasing. At present, that scale then represents 31.25/0.71= 44 Mpc. Does that seem correct?
There may be another problem; I expect the distances to scale with the scale factor "a", not with h (\propto \dot{a}/a). For example, from 1 Gyr to the present, h has changed by ratio ~9, whereas a has changed by ratio ~6.5, and I would think that the scale in the t = 1 Gyr image
http://www.mpa-garching.mpg.de/galform/virgo/millennium/seqF_019a_half.jpg
should represent 1/6.5 (not 1/9) of the scale in the z = 0 image. Does this seem correct?

 

[Jorrie]

Mpc/h and [31.25/h] Mpc are basically the same thing. This is comoving distance, which does not change with the evolution of h (or a), because it is present proper distance. I think the h is there to cater for the uncertainty in h, which may soon be revised upwards to around 0.74, yet they do not have to alter the scale of their simulation.

 

[BillSaltLake]

Note that h (\propto H) and a have different time evolution. Therefore a parameter that scales with h does not scale with a, and comoving distance scales with a. I think that the scale in the image should read "44/(1+z) Mpc", noting that 1/(1+z) \propto a.

 

[Jorrie]

... Therefore a parameter that scales with h does not scale with a, and comoving distance scales with a. I think that the scale in the image should read "44/(1+z) Mpc", noting that 1/(1+z) \propto a.

The picture is for z=0 (today), so it could have read either 44 Mpc (h=0.71), or 31.25 Mpc/h. The latter value remains constant when h (= H0/100) is refined by observation. Cosmologists use this so that their reports do not have to be updated as better values of H0 become accepted. AFAIK, h refers only to H0 and hence does not evolve with a. The parameter evolving with a is usually referred to as H(t).

BTW, although not applicable here, I thought it is proper distance that scales with a and comoving distance is constant for a given galaxy.