Does the Hubble expansion cause apparent friction? When you have a peculiar velocity (i.e. a velocity that is not due to the expansion of the universe) your current comoving frame (i.e. the frame of reference relative to the stuff directly around you) is always changing.  Your new frames always have some velocity in the direction of your travel relative to your old frames (at least as long as the Hubble constant is positive, but this is the case in the current universe and AFAIK is expected to never change).  If you measure your velocity always relative to your current comoving frame, your velocity should decrease therefore.
Does this "Hubble friction" (in quotes because that term is already in use for something else) actually exist (and is not canceled out perfectly by e.g. the acceleration due to expansion or something) and how big is it.  I tried to derive the formula myself, but my understanding of this concept is too bad to be able to do it and I also didn't find anything searching the web.
 A: The effect is real, and happens for the reason you describe, but it is a kinematic process, not frictional. Peebles mentions it in Principles of Physical Cosmology and calls it "velocity sorting". E. A. Milne, who may have been the first to discuss it in the 1930s, also described it as a sorting process.
Suppose your object is at the origin at time $t$ and it has velocity $v$ relative to local inertial coordinates, which is also its peculiar velocity. A short time $dt$ later (short enough that it's still on the local inertial patch), its velocity is still $v$, but its location is $v\,dt$; its peculiar velocity at time $t+dt$ is therefore $v - H\,v\,dt$. That argument gives $dv/dt = -Hv$ (for small $v$).
A: The relativistic momentum $p=mv\gamma$ relative to a local observer comoving with the Hubble flow is inversely proportional to the growth of the scale factor $a$:
$$\frac{p_0}{a(t)} = \frac{p(t)}{a_0}$$
With photons that relation also holds, but since their $v$ is constant the frequency decreases instead in order to shrink their momentum.
