First of all, there IS a preferred rest frame, the CMB frame. If you are in that frame, the CMB (cosmic microwave background radiation) is uniform in all directions. If you are in any other frame, then the CMB is doppler shifted and looks bluer in the direction you are moving, and redder in other direction. From http://en.wikipedia.org/wiki/Cosmic_microwave_background#CMBR_dipole_anisotr... : "From the CMB data it is seen that our local group of galaxies (the galactic cluster that includes the Solar System's Milky Way Galaxy) appears to be moving at 369+-0.9 km/s relative to the reference frame of the CMB" From http://en.wikipedia.org/wiki/Milky_Way : it claims milky way is moving at 552 km/sec versus CMB. http://en.wikipedia.org/wiki/Andromeda_Galaxy Milky Way & Andromeda are approaching each other at about 140 km/sec and will collide. This all is a very small speed compared to c = 299792 km/sec. Our speed is less than 0.002 c. Also note, the escape velocity from our galaxy from here, is about 500 km/sec, (larger if wanted to escape from the core) so these speeds are of the same order as you would naively expect for gravitational reasons, and the virial theorem. What is the source of all these speeds? Ultimately, it comes from fluctuations in the early universe. These small fluctuations can still be seen in the CMB sky maps produced by WMAP and planck satellite. In a perfectly uniform universe there would be no speed and density fluctuations. These initial fluctuations self-amplified via gravitational effects. What actually seems much more surprising to me is the existence of vast "jets" moving at relativistic speeds, thought to be ejected from black holes as a side effect of infall and relativistic magneto-hydrodynamics somehow.