Power spectrum of large-scale magnetic fields from Gravitoelectromagnetic inflation with a decaying cosmological parameter

Introducing a variable cosmological parameter $\mathrm{\Lambda }(t)$ in a geometrical manner from a 5D Riemann-flat metric, we investigate the origin and evolution of primordial magnetic fields in the early universe, when the expansion is governed by a cosmological parameter $\mathrm{\Lambda }(t)$ that decreases with time. Using the gravitoelectromagnetic inflationary formalism, but without the Feynman gauge, we obtain the power of spectrums for large-scale magnetic fields and the inflaton field fluctuations during inflation. A very important fact is that our formalism is {\em naturally non-conformally invariant}.