Cosmic Microwave Background Dipole Asymmetry could be explained by Axion Monodromy Cosmic Strings

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.