Kernel-Based Emulator for the 3D Matter Power Spectrum from CLASS
  The 3D matter power spectrum, $P_{\delta}(k,z)$ is a fundamental quantity in
the analysis of cosmological data such as large-scale structure, 21cm
observations, and weak lensing. Existing computer models (Boltzmann codes) such
as CLASS can provide it at the expense of immoderate computational cost. In
this paper, we propose a fast Bayesian method to generate the 3D matter power
spectrum, for a given set of wavenumbers, $k$ and redshifts, $z$. Our code
allows one to calculate the following quantities: the linear matter power
spectrum at a given redshift (the default is set to 0); the non-linear 3D
matter power spectrum with/without baryon feedback; the weak lensing power
spectrum. The gradient of the 3D matter power spectrum with respect to the
input cosmological parameters is also returned and this is useful for
Hamiltonian Monte Carlo samplers. The derivatives are also useful for Fisher
matrix calculations. In our application, the emulator is accurate when
evaluated at a set of cosmological parameters, drawn from the prior, with the
fractional uncertainty, $\Delta P_{\delta}/P_{\delta}$ centred on 0. It is also
$\sim 300$ times faster compared to CLASS, hence making the emulator amenable
to sampling cosmological and nuisance parameters in a Monte Carlo routine. In
addition, once the 3D matter power spectrum is calculated, it can be used with
a specific redshift distribution, $n(z)$ to calculate the weak lensing and
intrinsic alignment power spectra, which can then be used to derive constraints
on cosmological parameters in a weak lensing data analysis problem. The
software ($\texttt{emuPK}$) can be trained with any set of points and is
distributed on Github, and comes with a pre-trained set of Gaussian Process
(GP) models, based on 1000 Latin Hypercube (LH) samples, which follow roughly
the current priors for current weak lensing analyses.
