Using machine learning to compress the matter transfer function T (k)

Abstract

The linear matter power spectrum P(k,z) connects theory with large scale structure observations in cosmology. Its scale dependence is entirely encoded in the matter transfer function T(k), which can be computed numerically by Boltzmann solvers, and can also be computed semianalytically by using fitting functions such as the well-known Bardeen-Bond-Kaiser-Szalay (BBKS) and Eisenstein-Hu (EH) formulas. However, both the BBKS and EH formulas have some significant drawbacks. On the one hand, although BBKS is a simple expression, it is only accurate up to 10%, which is well above the 1% precision goal of forthcoming surveys. On the other hand, while EH is as accurate as required by upcoming experiments, it is a rather long and complicated expression. Here, we use the genetic algorithms (GAs), a particular machine learning technique, to derive simple and accurate fitting formulas for the transfer function T(k). When the effects of massive neutrinos are also considered, our expression slightly improves over the EH formula, while being notably shorter in comparison.