Is the Universe Mirror Symmetric on the Cosmological Scale?

In 1956, the experimental discovery that the weak interaction of particle physics violated the conservation of parity (that all the laws of physics are invariant when observed in a mirror) stunned physicists. All of the other fundamental forces: gravity, electromagnetism, and the strong nuclear force, were observed to conserve parity (or at least there was no evidence they didn’t), and yet here was a force that refused to behave. It took years before it was understood why this is.

But does the universe conserve parity at the very largest scale? Observations of the distribution and spins of galaxies and of the cosmic microwave background radiation provide hints it may not. Is there really something there and, if so, what does it mean?