Information content in the halo-model dark-matter power spectrum

Using the halo model, we investigate the cosmological Fisher information in the non-linear dark-matter power spectrum about the initial amplitude of linear power. We find that there is little information on ‘translinear’ scales (where the one- and two-halo terms are both significant) beyond what is on linear scales, but that additional information is present on small scales, where the one-halo term dominates. This behaviour agrees with the surprising results that Rimes & Hamilton found using N-body simulations. We argue that the translinear plateau in cumulative information arises largely from fluctuations in the numbers of large haloes in a finite volume. This implies that more information could be extracted on non-linear scales if the masses of the largest haloes in a survey are known.