Canonically rescaled de Sitter scalar mode
= Canonically rescaled de Sitter scalar mode
{c}
For $a=-1/(H_{\rm inf}\tau)$, the rescaled mode
$$
\widetilde\phi_{\mathbf k}=a\widehat\phi_{\mathbf k}
$$
satisfies
$$
\widetilde\phi_{\mathbf k}''
+\left(c^2k^2-\frac2{\tau^2}\right)
\widetilde\phi_{\mathbf k}=0.
$$