  We present a general framework for obtaining robust bounds on the nature of
dark matter using cosmological $N$-body simulations and Lyman-alpha forest
data. We construct an emulator of hydrodynamical simulations, which is a
flexible, accurate and computationally-efficient model for predicting the
response of the Lyman-alpha forest flux power spectrum to different dark matter
models, the state of the intergalactic medium (IGM) and the primordial power
spectrum. The emulator combines a flexible parameterization for the small-scale
suppression in the matter power spectrum arising in "non-cold" dark matter
models, with an improved IGM model. We then demonstrate how to optimize the
emulator for the case of ultra-light axion dark matter, presenting tests of
convergence. We also carry out cross-validation tests of the accuracy of flux
power spectrum prediction. This framework can be optimized for the analysis of
many other dark matter candidates, e.g., warm or interacting dark matter. Our
work demonstrates that a combination of an optimized emulator and cosmological
"effective theories," where many models are described by a single set of
equations, is a powerful approach for robust and computationally-efficient
inference from the cosmic large-scale structure.
