= Conformal-time quadratic action for an inflaton perturbation
{title2=$S^{(2)}=\tfrac12\int d\tau\,d^3x\{(f')^2-(\nabla f)^2+(a''/a-a^2V'')f^2\}$}
Neglecting metric perturbations, the rescaling $f=a\delta\phi$ removes the expansion friction from the scalar perturbation action after a boundary term is discarded. Its canonical momentum is $f'$, and each real Fourier oscillator has time-dependent squared frequency $k^2+a^2V''-a''/a$. The oscillator can become inverted on <superhorizon scales>; the canonical commutation relations still apply.
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