Primordial electric fields before recombination in the early Universe

This work is a supplement on the previous research about primordial electromagnetic fields. In this work, three important problems are discussed: the evolution of primordial electric fields, the electric and particle densities' solitons in plasma before recombination and their influences on the power spectra of cosmic microwave background. Detailed computations show that the primordial electric fields dissipate by Landau damping effect on both large scale and small scale and there is no impact on the spectrum. While, before recombination, there exist solitary waves stably propagating in plasma whose speed is significantly slower than that of baryonic acoustic oscillations, working only at extremely small scale. On the other hand, the amplitude of solitons is so weak that only a significantly small contribution on the phase of baryon acoustic oscillations, so there merely exist the messages about such electric solitary waves on the spectrum. In a word, as relevant monographs on cosmology, neglecting the electromagnetic fields (electric fields at least) is a reasonable treatment on the calculations of cosmic microwave background. However, the protonic density fluctuations show a form of KdV equation while its propagation as a stable solitary wave, leading a probability to the origin of fluctuation promoting the generation and evolution of galaxies.