On the information content of the matter power spectrum

Understand

We discuss an analytical approximation for the matter power spectrum covariance matrix and its inverse on translinear scales, $k \sim 0.1h - 0.8h/\textrm{Mpc}$ at $z = 0$.

• We proceed to give an analytical expression for the Fisher information matrix of the nonlinear density field spectrum, and derive implications for its cosmological information content.
• We find that the spectrum information is characterized by a pair of upper bounds, 'plateaux', caused by the trispectrum, and a 'knee' in the presence of white noise.
• The effective number of Fourier modes, normally growing as a power law, is bounded from above by these plateaux, explaining naturally earlier findings from $N$-body simulations.