Faster cosmological analysis with power spectrum without simulations

$$Future surveys could obtain tighter constraints on the cosmological parameters with the galaxy power spectrum than with the Cosmic Microwave Background. However, the inclusion of multiple overlapping tracers, redshift bins, and more non-linear scales means that generating the necessary ensemble of simulations for model-fitting presents a computational burden. In this work, we combine full-shape fitting of galaxy power spectra, analytical covariance matrix estimates, the MOPED (Massively Optimised Parameter Estimation and Data compression) method, and the Taylor expansion interpolation of the power spectrum for the first time to constrain the cosmological parameters directly from a state-of-the-art set of galaxy clustering measurements. We find it takes less than a day to compute the analytical covariance while it takes several months to calculate the simulated ones. Combining MOPED with the Taylor expansion interpolation of the power spectrum, we can constrain the cosmological parameters in just a few hours instead of a few days. We also find that even without a priori knowledge of the best-fit cosmological or galaxy bias parameters, the analytical covariance matrix with the MOPED compression still gives consistent cosmological constraints to within 0.1$\sigma$ after two iterations. Therefore, the pipeline we have developed here can significantly speed up the analysis for future surveys such as DESI and Euclid.