Information content of the non-linear matter power spectrum

We use an ensemble of N-body simulations of the currently favoured (concordance) cosmological model to measure the amount of information contained in the non-linear matter power spectrum about the amplitude of the initial power spectrum. Two surprising results emerge from this study: (i) that there is very little independent information in the power spectrum in the translinear regime (k≃ 0.2 –0.8 h Mpc−1 at the present day) over and above the information at linear scales; and (ii) that the cumulative information begins to rise sharply again with increasing wavenumber in the non-linear regime. In the fully non-linear regime, the simulations are consistent with no loss of information during translinear and non-linear evolution. If this is indeed the case then the results suggest a picture in which translinear collapse is very rapid, and is followed by a bounce prior to virialization, impelling a wholesale revision of the HKLM–Peacock & Dodds formalism.

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