PkANN: Non-Linear Matter Power Spectrum Interpolation through Artificial Neural Networks

Abstract

We investigate the interpolation of power spectra of matter fluctuations using artificial neural networks (ANNs). We present a new approach to confront small-scale non-linearities in the matter power spectrum. This ever-present and pernicious uncertainty is often the Achilles&rsquo heel in cosmological studies and must be reduced if we are to see the advent of precision cosmology in the late-time Universe. We detail how an accurate interpolation of the matter power spectrum is achievable with only a sparsely sampled grid of cosmological parameters. We show that an optimally trained ANN, when presented with a set of cosmological parameters (&Omegam h2, &Omegab h2, ns, w0, &sigma8, ∑m&nu and z), can provide a worst-case error &le 1 per cent (for redshift z &le 2) fit to the non-linear matter power spectrum deduced through large-scale N-body simulations, for modes up to k &le 0.9 h Mpc-1. Our power spectrum interpolator, which we label &lsquo PkANN &rsquo, is designed to simulate a range of cosmological models including massive neutrinos and dark energy equation of state w0 ≠ -1. PkANN is accurate in the quasi-non-linear regime (0.1 h Mpc-1 &le k &le 0.9 h Mpc-1) over the entire parameter space and marks a significant improvement over some of the current power spectrum calculators. The response of the power spectrum to variations in the cosmological parameters is explored using PkANN. Using a compilation of existing peculiar velocity surveys, we investigate the cosmic Mach number statistic and show that PkANN not only successfully accounts for the non-linear motions on small scales, but also, unlike N-body simulations which are computationally expensive and/or infeasible, it can be an extremely quick and reliable tool in interpreting cosmological observations and testing theories of structure-formation.