On the Possible Enhancement of the Global $21$-cm Signal at Reionization from the Decay of Cosmic String Cusps

Abstract: We consider cosmic string cusp annihilations as a possible source of enhancement to the global background radiation temperature in $21$-cm photons at reionization. A soft photon spectrum is induced via the Bremsstrahlung and Synchrotron emission of electrons borne out of QCD jets formed off the cusp. The maximal energy density background comes from synchrotron induced photons with a string tension of $G\mu \sim 10^{-18}$. In this instance, the radiation background at reionization is heated up by $5\cdot 10^{-3} \,\, K$. We find that the depth of the absorption trough ($\delta T_b$) in $21$-cm at reionization is altered by one part in $10^4$ from the strings, requiring high precision measurements to be detectable. This mechanism cannot explain the $\delta T_b$ observed by the EDGES experiment.