Sachs-Wolfe plateau
= Sachs-Wolfe plateau
{c}
{title2=$\ell(\ell+1)C_\ell=\mathrm{constant}$}
For a scale-invariant potential spectrum with $\mathcal A_\Phi=k^3P_\Phi/(2\pi^2)$ constant, the matter-era <Sachs-Wolfe effect> gives $C_\ell=(4\pi\mathcal A_\Phi/9)\int j_\ell(x)^2dx/x$. The <logarithmic spherical Bessel square integral> then gives $\ell(\ell+1)C_\ell=2\pi\mathcal A_\Phi/9$. This plateau applies to large-angle temperature anisotropies, neglecting acoustic evolution and late evolving potentials; it is not a constant $C_\ell$ spectrum.