Using machine learning to compress the matter transfer function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
J. Bayron Orjuela-Quintana, Savvas Nesseris, Wilmar Cardona
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.