Canonical rescaling of a scalar cosmological perturbation
= Canonical rescaling of a scalar cosmological perturbation
{title2=$v=a\delta\chi$}
Neglecting <metric perturbations>, a free massive <scalar field> fluctuation obeys $\delta\chi''+2\mathcal H\delta\chi'-\nabla^2\delta\chi+a^2m^2\delta\chi=0$. Rescaling it by the <scale factor> removes the conformal-time friction and gives $v''-\nabla^2v+(a^2m^2-a''/a)v=0$. Growth of $v$ need not mean growth of the physical fluctuation $v/a$.