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

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 by focusing on $h$-independent cosmological parameters, which can be separated into those defining the linear power spectrum shape ($\mathbf{\Theta}_{\mathrm{s}}$) and those affecting only its amplitude evolution ($\mathbf{\Theta}_{\mathrm{e}}$). 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 ($\mathbf{\Theta}_{\mathrm{s}}$) 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 $0.2 < \sigma_{12} < 1.0$, providing predictions for $0.006\,{\rm Mpc}^{-1} < k < 2\,{\rm Mpc}^{-1}$. We validate Aletheia against N-body simulations, demonstrating sub-percent accuracy. When tested on a suite of dynamic dark energy models, the full emulator's predictions show a variance of approximately 0.2%, a factor of five smaller than that of the state-of-the-art EuclidEmulator2 (around 1% variance). Furthermore, Aletheia maintains sub-percent accuracy for the best-fit dynamic dark energy cosmology from recent 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.