Origin of Cosmic Magnetic Fields

We calculate, in the free Maxwell theory, the renormalized quantum vacuum expectation value of the two-point magnetic correlation function in de Sitter inflation. We find that quantum magnetic fluctuations remain constant during inflation instead of being washed out adiabatically, as usually assumed in the literature. The quantum-to-classical transition of super-Hubble magnetic modes during inflation allow us to treat the magnetic field classically after reheating, when it is coupled to the primeval plasma. The actual magnetic field is scale independent and has an intensity of $\mathrm{\text{few}}\times {10}^{-12}\mathrm{G}$ if the energy scale of inflation is $\mathrm{\text{few}}\times {10}^{16}\mathrm{GeV}$. Such a field accounts for galactic and galaxy cluster magnetic fields.