Gravitoelectromagnetic inflation and seeds of cosmic magnetic fields from geometrical Weyl-invariant scalar-tensor theory of gravity

We investigate cosmological inflationary scenarios from a gravitoelectromagnetic theory. Our work is formulated in the light of a recently introduced geometrical Weyl-Invariant scalar-tensor theory of gravity, where the nature of both the electromagnetic potential and the inflaton field is attributed to the space-time geometry. We obtain a Harrison-Zeldovich power spectrum for quantum fluctuations of the inflaton field. In our model the electromagnetic fields have also a nearly scale invariant power spectrum for a power-law inflation. We found that the the seed magnetic fields have a nearly scale invariant power spectrum and generate in the present times cosmic magnetic fields of the order $\lesssim 10^{9}$ gauss, in good agreement with CMB observations.