Why CBR and Comoving coordinates are not absolute reference frames? Let us say that we know the Hubble parameter now. Why cannot Cosmic Background Radiation and/or the Comoving 3D frame be taken as absolute reference frames (at least far enough from massive bodies, if this is relevant)?
In such frames and continuously correcting via the scale factor, objects to which no force is applied are at rest. This seems to me an absolute inertial reference frame big at least as the observable universe.
Please try to explain me what I do wrong with this reasoning taking into account that my technical knowledge of GR is basically zero. 
Edit: for instance who is travelling between the twins of the paradox will be the one  changing comoving coordinates. He does so by firing rockets but the same could be deduced on purely kinematic bases.
 A: I think I could self answer as far CBR is concerned. We move with respect to CBR by virtue of space expansion. Any other, such having a proper speed, does not modify our distance to CBR which is ubiquitous.
My question is still open concerning comoving coordinate, which seems to me a grid that in principle extends beyond the observable universe.
A: You can call that reference frame "absolute" if you want, but it's just a word. Applying a label to the frame doesn't imbue it with extra physical properties. Its physical properties (like isotropy) are due to the matter distribution. If you removed the matter from a region of spacetime, there would no longer be anything special about the frame of isotropy of the (no longer present) background radiation in that region.

for instance who is travelling between the twins of the paradox will be the one changing comoving coordinates.

You seem to be presupposing that the inertially moving twin is stationary in the comoving frame. That needn't be true. Even if it is true, you can still choose some other reference frame to do your calculations, and you'll get the same answer for any physically meaningful quantity that you calculate (such as the age difference of the twins when they reunite).
