Scale-invariant inflationary power spectrum
= Scale-invariant inflationary power spectrum
A Fourier-space variance $P_k$ in three dimensions is scale invariant when the dimensionless power per logarithmic wavenumber interval,
$$
\Delta^2(k)=\frac{k^3P_k}{2\pi^2},
$$
is independent of $k$. For a massless inflaton mode at late times,
$$
P_k\longrightarrow\frac{\hbar H_{\rm inf}^2}{2c^3k^3},
$$
so $\Delta^2(k)$ is constant.