Hubble's constant measured by observer approaching light speed

Question

I recently read about expansion of the universe and I can't figure out if Hubble's law (and other models of expansion of the universe) is compatible with the theory of relativity.

My question is: In which point of reference is recessional velocity between two bodies proportional to the distance between them ($v=HD$) with '$H$', Hubble constant? Imagine two observers moving in relation to each other with great speed. Each observer attempts to measure the local value of Hubble's constant by placing around himself two non-interacting particles and continuously checking distance between them (let's assume that all external fields and forces are somehow eliminated). Hubble's law states that the particles will move away in time with $v=HD$ and the theory of relativity states that each observer will see that the other one's clock slowed down, so the other one's $H$ will seem to be lower than his own.

So far everything seems ok, but from above scenario it seems that the expansion is a feature of particles (matter) instead of the space itself. If the above scenario is correct that means that for example it should be possible to avoid or postpone "big rip" by moving moving very fast and slowing one's clock (and local recessional velocity); but moving fast in reference to what?

On the other hand, if two observers measure different Hubble's constant because of their speed, that would mean that there is some universal point of reference in which $H$ is smallest, and that point of reference would define absolute rest. All observers moving in relation to this point of reference should observe higher $H$ because their clocks run slower. That doesn't seems right either.

When scientists talk about the rate of expansion of the universe, in which point of reference (with whose clock) is this rate measured?

Answer 1

The preferred frame of reference is that of the co-moving reference frame that defines the Hubble flow. In practical terms that can be defined by correcting any velocity for the observer's motion with respect to the cosmic microwave background. Individual peculiar velocities for galaxies (including our own) are measured in hundreds to thousands of km/s. This is not large enough to make much difference to any practical measurement of the Hubble constant, but of course leads to scatter in the Hubble diagram for galaxies where $H_0 d$ is not much greater than the typical peculiar velocity.

Possibly your confusion arises from the term "recession velocity". As Orca commented, this is a poor nomenclature, implying that things are flying apart from each other. In fact, a better picture is to think of each galaxy embedded in its own little bit of space, each moving with a relatively modest peculiar velocity with respect to the cosmic microwave background. However, the space between the galaxies is expanding. It is this expansion (and also the additional expansion that occurs whilst light travels between galaxies) that gives the impression of relative motion (and indeed the redshift is spectroscopically indistinguishable from a doppler effect caused by relative motion).

Reading this short essay might help.