Effect of σ₈ variations on the matter–matter power spectrum (left) and on the matter–electron pressure power spectrum (right) at z = 0. We show halo model power spectra for σ₈ = 0.7 (blue) to σ₈ = 0.9 (red) divided by a central σ₈ = 0.8 model. For linear theory the plot would simply be horizontal lines. We see that boosting the amplitude of fluctuations increases the amplitude of the matter–electron power spectrum far more than it does for the matter-matter. At a wavenumber of ≃1 h Mpc⁻¹ the matter-matter power spectrum scales like while matter–electron pressure scales like . This is because the electron pressure field is dominated by high-mass haloes from the tail of the mass function that are very sensitive to the linear power spectrum amplitude.