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Abstract Renormalization scheme of quantum electrodynamics (QED) at high temperatures is used to calculate the effective parameters of relativistic plasma in the early universe. Renormalization constants of QED play the role of effective parameters of the theory and can be used to determine the collective behavior of the medium. We explicitly show that the dielectric constant, magnetic reluctivity, Debye length and the plasma frequency depend on temperature in the early universe. Propagation speed ( $$v_{prop}$$ v prop ), refractive index ( $$i_r$$ i r ), plasma frequency ( $$\omega $$ ω ) and Debye shielding length ( $$\lambda _D$$ λ D ) of a QED plasma are computed at extremely high temperatures in the early universe. We also found the favorable conditions for the existence of relativistic plasma from these calculations.