In inflationary magnetogenesis with inhomogeneous inflaton perturbations, the claimed new scale-invariance conditions and spectral-index shifts rest on a derivation step that treats integration constants as time-dependent and drops a same-order source term.
However, this restricts the form of the coupling function—it must ensure the con- sistency of the theory
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The Impact of Inhomogeneous Perturbations of the Inflaton on the Cosmological Primordial Magnetic Field
In inflationary magnetogenesis with inhomogeneous inflaton perturbations, the claimed new scale-invariance conditions and spectral-index shifts rest on a derivation step that treats integration constants as time-dependent and drops a same-order source term.