  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 few \times 10^(-12) G if the
energy scale of inflation is few \times 10^(16) GeV. Such a field accounts for
galactic and galaxy cluster magnetic fields.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology