We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly so that two randomly chosen particles are unlikely to be directly entangled with each other - the reduced density matrix describing any pair is likely to be separable.
Buniy, R.V., & Hsu, S.D.H. (2012). Everything is entangled. Physics Letters B, 718(2): 233-236. doi: 10.1016/j.physletb.2012.09.047