Aletheia : emulating the non-linear matter power spectrum in the context of evolution mapping

ABSTRACT We present aletheia, a new emulator of the non-linear matter power spectrum, $P(k)$, built upon the evolution mapping framework. This framework addresses the limitations of traditional emulation, the need to densely sample high-dimensional parameter spaces, by focusing on h-independent cosmological parameters, which can be separated into those defining the linear power spectrum shape ($\boldsymbol {\Theta }_{\mathrm{s}}$) and those affecting only its amplitude evolution ($\boldsymbol {\Theta }_{\mathrm{e}}$). The combined impact of evolution parameters and redshift is compressed into a single amplitude parameter, $\sigma _{12}$. aletheia uses a two-stage Gaussian Process emulation: a primary emulator predicts the non-linear boost factor as a function of ($\boldsymbol {\Theta }_{\mathrm{s}}$) and $\sigma _{12}$ for fixed evolution parameters, while a second one applies a small linear correction based on the integrated growth history. The emulator is trained on shape parameters spanning $\pm 5\sigma$ of Planck constraints and a wide clustering range $0.2 \lt \sigma _{12} \lt 1.0$, providing predictions for $0.006\, {\rm Mpc}^{-1} \lt k \lt 2\, {\rm Mpc}^{-1}$. We validate aletheia against N-body simulations, demonstrating sub-per cent accuracy. When tested on a suite of dynamic dark energy models, the full emulator’s predictions show a variance of approximately 0.2 per cent, a factor of five smaller than that of the state-of-the-art euclidemulator2 (around 1 per cent variance). Furthermore, aletheia maintains sub-per cent accuracy for the best-fitting dynamic dark energy cosmology from recent Dark Energy Spectroscopic Instrument (DESI) data, a model whose parameters lie outside the training ranges of most conventional emulators. This demonstrates the power of the evolution mapping approach, providing a robust and extensible tool for precision cosmology.