We use the f ^ { 2 } FF model to study the generation of primordial magnetic fields ( PMF ) in the context of large field inflation ( LFI ) , described by the potential , V \sim M \phi ^ { p } .
We compute the magnetic and electric spectra for all possible values of the model parameters under de Sitter and power law expansion .
We show that scale invariant PMF are not obtained in LFI to first order in the slow roll approximation , if we impose the constraint V ( \phi = 0 ) \sim 0 .
Alternatively , if these constraints are relaxed , the scale invariant PMF can be generated .
The associated electric field energy can fall below the energy density of inflation , \rho _ { Inf } for the ranges of comoving wavenumbers , k > 8 \times 10 ^ { -7 } { Mpc ^ { -1 } } and k > 4 \times 10 ^ { -6 } { Mpc ^ { -1 } } in de Sitter and power law ( PL ) expansion .
Further , it can drop below \rho _ { Inf } on the ranges , e-foldings N > 51 , p < 1.66 , p > 2.03 , l _ { 0 } > 3 \times 10 ^ { 5 } { M _ { Pl } } ^ { -1 } ( H _ { i } < 3.3 \times 10 ^ { -6 } M _ { Pl } ) , and M > 2.8 \times 10 ^ { -3 } M _ { Pl } .
All of the above ranges fit with the observational constraints .