Basically, on a cosmological scale, distance and velocity are connected

yeah btw to comment on this: this phenomenon is probably more important than it seems at first glance. because it implies that, while there is neither an absolute position nor an absolute velocity in relativity theory, there is a connection between position and velocity. so, for each position in space, there is an associated zero velocity, or reference velocity, which is the velocity of the cosmos at that location. or at least that’s what i’m lead to believe.

now, this is not at all obvious. one might argue that that’s bullshit, frankly, but it appears at least 3 times in various aspects of standard models of cosmology:

• for one, contemporary microwave background. it’s said to be isotropic (and has the shape of a black body radiation) but only if the observer moves with a certain velocity. if you move extremely fast in either way, one side gets blueshifted while the other one gets redshifted, so it’s not isotropic anymore. there’s exactly one (finite!) velocity for which it is most isotropic, which is the “average velocity” of the radiation.
• then there’s the whole question of how a vacuum energy could possibly be lorentz-invariant. the way i see it, if there is radiation in space everywhere, then that would have to be similar to microwave background (just at another frequency). so it again would have to have a certain average velocity. note that this is different from the previous point because while the previous point uses other objects as reference frame (that might not be present in an alternative universe), this one does not. you cannot have a universe with the same laws as ours that’s completely empty of vacuum energy, so there’s always some reference frame.
• then there’s the issue that if you go really far back in time, the cosmic expansion is not lorentz-invariant. well, at least not if you look at this curve:

Image

if you tilt it somewhat, it’s not isotropic anymore. because while expansion rate is accepted to vary with time, it should be homogenous in space. now, if you do a lorentz-transformation, these two things cannot hold at the same time. so, cosmic expansion wouldn’t be lorentz-invariant?