The Cosmic Background Radiation experiment (COBE 2006) data indicated that overall rotation of the universe was zero, which was within the limits of accuracy of the instrument.
In 1949, Kurt Gödel proved the existence of solutions involving closed time-like curves, to Albert Einstein's field equations within the Theory of General Relativity. His solution required a rotating universe, which would allow time travel to the past and caused Einstein to have doubts about his own theory. His solutions are known as the Gödel metric. Hollywood time travel stories are very popular 'Star Trek IV' etc. However, time traveller's from the future are either very discrete or choose to come to our period (I don't blame them!). Or the universe does not rotate significantly, as indicated by COBE.