Fast Approximate Model for the 3D Matter Power Spectrum

Many Bayesian inference problems in cosmology involve complex models. Despite the fact that these models have been meticulously designed, they can lead to intractable likelihood and each forward simulation itself can be computationally expensive, thus making the inverse problem of learning the model parameters a challenging task. In this paper, we develop an approximate model for the 3D matter power spectrum, P(k,z), which is a central quantity in a weak lensing analysis. An important output of this approximate model, often referred to as surrogate model or emulator, are the first and second derivatives with respect to the input cosmological parameters. Without the emulator, the calculation of the derivatives requires multiple calls of the simulator, that is, the accurate Boltzmann solver, CLASS. We illustrate the application of the emulator in the calculation of different weak lensing and intrinsic alignment power spectra and we also demonstrate its performance on a toy simulated weak lensing dataset.