 Dimensionless cosmological power spectrum

The dimensionless spectrum is the contribution to a statistically isotropic field variance per logarithmic wavenumber interval: $⟨X^2⟩=\int d\log k{\Delta }_X(k)$, with any necessary smoothing or regulators. Some conventions denote this same quantity ${\Delta }_X^2$. The definition, not the superscript convention, fixes its meaning.