Primordial magnetic fields in the $f^{2}FF$ model in large field
  inflation under de Sitter and power law expansion
  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, $\rho_{\rm{Inf}}$ for the ranges of
comoving wavenumbers, $ k > 8 \times 10^{-7} \rm{Mpc^{-1}}$ and $ k > 4 \times
10^{-6} \rm{Mpc^{-1}}$ in de Sitter and power law (PL) expansion. Further, it
can drop below $\rho_{\rm{Inf}}$ on the ranges, e-foldings $N > 51$, $p<1.66$,
$p >2.03$, $l_0 > 3 \times 10^5 {M_{\rm{Pl}}}^{-1} (H_i < 3.3 \times 10^{-6}
M_{\rm{Pl}})$, and $M > 2.8 \times 10^{-3} M_{\rm{Pl}}$. All of the above
ranges fit with the observational constraints.
