Baryogenesis via density fluctuations with a second-order electroweak phase transition

We consider the presence of cosmic string-induced density fluctuations in the early universe at temperatures below the electroweak phase transition temperature. Resulting temperature fluctuations can restore the electroweak symmetry locally, depending on the amplitude of fluctuations and the background temperature. The symmetry will be spontaneously broken again in a given region as the temperature drops there (for fluctuations with length scales smaller than the horizon), resulting in the production of baryon asymmetry. The time-scale of the transition will be governed by the wavelength of fluctuation and, hence, can be much smaller than the Hubble time. This leads to strong enhancement in the production of baryon asymmetry for a second-order electroweak phase transition as compared to the case when transition happens due to the cooling of the universe via expansion. For a two-Higgs doublet model (with appropriate CP violation), we show that one can get the required baryon asymmetry if fluctuations propagate without getting significantly damped. If fluctuations are damped rapidly, then a volume factor suppresses the baryon production, though it is still 3–4 orders of magnitude larger than the conventional case of second-order transition.