  Observations by the Wilkinson Microwave Anisotropy Probe and the Planck
mission suggest a hemispherical power amplitude asymmetry in the cosmic
microwave background, with a correlation length on the order of the size of the
observable Universe. We find that this anomaly can be naturally explained by an
axion-like particle (ALP) cosmic string formed near our visible Universe. The
field variation associated to this cosmic string creates particle density
fluctuations after inflation, which consequently decay into radiation before
the Big Bang Nucleosynthesis (BBN) era and resulted in the observed power
asymmetry. We find in this scenario that the hemispherical power amplitude
asymmetry is strongly scale dependent: $A(k)\propto {\rm exp}(-kl)/k$.
Admittedly, typical inflation models predict a relic number density of
topological defects of order one per observable Universe and so in our model
the cosmic string must be tuned to have an impact factor of order $1/H_0$.
Interestingly, the constraints based on purely cosmological considerations also
give rise to a Peccei-Quinn scale $F_a$ of order $10^3$ larger then the Hubble
scale of inflation $H_I$. Assuming $H_I\sim 10^{13}$GeV, we then have an ALP
with $F_a\sim 10^{16}$GeV, which coincides with the presumed scale of grand
unification. As we require ALP decays occur before the BBN era, which implies a
relatively heavy mass or strong self-coupling, and considering that the
associated potential should break the shift symmetry softly in order to protect
the system from radiative corrections, we also conclude that the required ALP
potential should be monodromic in nature.
