Evolution of the primordial magnetic field from generation till today

In this presentation I will summarize our previous results concerning the evolution of primordial magnetic fields with and without helicity during the expansion of the Universe. I will address different magnetogenesis scenarios such as inflation, electroweak and QCD phase transitions magnetogenesis. A high Reynolds number in the early Universe ensures strong coupling between magnetic field and fluid motions. After generation the subsequent dynamics of the magnetic field is governed by decaying hydromagnetic turbulence. We claim that primordial magnetic fields can be considered as a seeds for observed magnetic fields in galaxies and clusters. Magnetic field strength bounds obtained in our analysis are consistent with the upper and lower limits of extragalactic magnetic fields.