If you're talking about a "global" comoving frame, then the 1 lyr ruler, which is rigid, will be shrinking by just over 1 mile/day. The photon will always take a year to travel the length of the ruler, even though the ruler will have "shrunk" ~430 miles WRT the global comoving frame during that...
The OP asked about the relative surface brightness of Earth vs. Saturn vs. Pluto when viewed close. Obviously an object will reduce in brightness if viewed from far away (specifically if the angular size is < 1 minute of arc, it cannot be resolved by the eye, so the farther away it is brought...
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.
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...
As with most things, one must be careful of definitions. I assume your coordinate system defines v=0 locally as 'at rest with respect to CMB'. However, there are two different ways that lengths (and time intervals) can then be defined. The "normal" way (such as CGS or MKS, for example)...
h has units of (mass)(length2)(time-1). If the time measurement unit is changing, then h must become variable, whether you let l units change in ratio with t units or keep l units constant. Similarly, E has units of ml2t-2, so if you keep c constant by letting l and t units vary in ratio, then E...
There's a possible problem here: he's saying (I think) that λLF2 is ~1/nμ where n is the # of phase space cells within the Hubble radius (and μ turns out to be ~1.2). However, during the matter era, n \propto ρ-3/4 \propto t3/2, which would make λ variable. This is not allowed in GR. (When I say...
The shrinkage atoms and gravitational orbits, with associated increase in atomic and orbital frequencies (to keep c constant) is a different but usable way to think of expansion. Note that if atoms and gravitational orbits were shrinking (at the same rate), we would not see the shrinking because...
What might be informative here is a plot of observations (or a plot derived from the millennium simulation) which shows the distribution of energy density. The x axis would be space volume, with the least dense on the left ("x"=0) and the most dense on the right ("x"=1 or 100%-- this is a...