The CMB Dipole Asymmetry suggests an Axion Like Particle with a $F_a$ of the GUT Scale

Observations made by the WMAP and the PLANK mission suggest a hemispherical power amplitude asymmetry in the cosmic microwave background (CMB) with a correlation length order of the observable universe. We find that this anomaly can be naturally explained with a cosmic string formed before inflation near the region of our universe. The cosmic string created a field variation around it which then turned into an energy density fluctuations after inflation. We find interestingly that the constraints of purely cosmological considerations give rise to a symmetry breaking scale of order $10^{16}$GeV, which is coincident with the GUT scale. In addition, a general axion like particle (ALP) typically retains a discrete shift symmetry $a\to a+2\pi F_a$ which gives rise to the mass and the self-coupling to the ALPs. If the self-coupling is relatively strong, the particles' effective mass in the condensate just after inflation is greatly enhanced so the ALPs decayed into radiation before the BBN era even their mass is very small in the vacuum.