Pearson's random walk in the space of the CMB phases: evidence for
  parity asymmetry
  The temperature fluctuations of the Cosmic Microwave Background (CMB) are
supposed to be distributed randomly in both magnitude and phase, following to
the simplest model of inflation. In this paper, we look at the odd and even
multipoles of the spherical harmonic decomposition of the CMB, and the
different characteristics of these, giving rise to a parity asymmetry. We
compare the even and odd multipoles in the CMB power spectrum, and also the
even and odd mean angles. We find for the multipoles of the power spectrum,
that there is power excess in odd multipoles, compared to even ones, meaning
that we have a parity asymmetry. Further, for the phases, we present a random
walk for the mean angles, and find a significant separation for even/odd mean
angles, especially so for galactic coordinates. This is further tested and
confirmed with a directional parity test, comparing the parity asymmetry in
galactic and ecliptic coordinates.
