We present our recent detailed calculation of the impacts from a background magnetic field on Big Bang Nucleosynthesis (BBN). Namely, the magnetic field impacts on the electron-positron thermodynamics, time temper-ature relation and the screening potential of the early Universe. Most interest-ingly, we investigated the electron-positron relativistic screening potential with the background magnetic field, such potential might lead to a non trivial effect on the electron capture reaction which could finally affect the neutron to proton ratio.
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