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

Details PkANN I: Non-Linear Matter Power Spectrum Estimation through Artificial Neural Networks PkANN I: Non-Linear Matter Power Spectrum Estimation through Artificial Neural Networks

2012-03-08

arxiv.org/abs/1203.1695v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

11 pages, 12 figures

Scientific paper

We investigate a new approach to confront small-scale non-linearities in the power spectrum of matter fluctuations. This ever-present and pernicious uncertainty is often the Achilles' heel in cosmological studies and must be reduced if we are to see the advent of precision cosmology in the late-time Universe. We show that an optimally trained Artificial Neural Network (ANN), when presented with a set of cosmological parameters ($\Omega_{\rm m} h^2, \Omega_{\rm b} h^2, n_s, w_0, \sigma_8, \sum m_\nu$ and redshift $z$), can provide a worst case accuracy ($\leq1%$ error for $z\leq2$) fit to the non-linear matter power spectrum deduced through $\it{N}$-Body simulations, for modes upto $k\leq0.7\,h\textrm{Mpc}^{-1}$. Our power spectrum predictor is accurate over the $\it{entire}$ parameter space for $z\leq2$. This is a significant improvement over some of the current matter power spectrum calculators. In this paper, we detail how an accurate prediction of the matter power spectrum is achievable with only a sparsely sampled grid of cosmological parameters. Unlike large-scale $\it{N}$-Body simulations which are computationally expensive and/or infeasible, a well-trained ANN can be an extremely quick and reliable tool in interpreting cosmological observations and parameter estimation. This paper is the first in a series. In this method paper, we generate the non-linear matter power spectra using {\sc halofit} and use them as mock observations to train the ANN. This work sets the foundation for Paper II, where a suite of $\it{N}$-Body simulations will be used to compute the non-linear matter power spectra at sub percent accuracy, in the quasi non-linear regime $(0.1\,h \textrm{Mpc}^{-1} \leq k \leq 0.9\,h \textrm{Mpc}^{-1})$ for redshifts between $z=0$ and $z=2$. A trained ANN based on this $\it{N}$-Body suite will be released for the scientific community.

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