Start with the following 3 statements... 1. If I were traveling through the cosmos at high velocity relative to the CMB I should observe the distances between stars and galaxies to be length contracted in the direction of my motion, but not in directions perpendicular to my travel. 2. The same laws of physics apply in all non-accelerating frames of reference 3. The universe, on large scales, in homogeneous (cosmological principal) How can all 3 of these statements be true? Any 2 are compatible, but I can't see how all 3 can be true at the same time? Secondly, I understand there is a limit to the size of our observable universe caused by the expansion of space. Objects further away are causally disconnected from us because they are receding from us at superluminal velocity. If I am traveling at high relativistic speed would I measure a different Hubble constant in my direction of travel then I would perpendicular to my direction of travel, essentially flattening my observable universe into a squished sphere? Or, would my universe still be spherical and regions which would otherwise be causally disconnected become connected due to my velocity?