Accelerating linear-theory clustering models: a new evolution-mapping based emulator

Large-scale structure observations are among the most powerful probes of the cosmological model. Their interpretation relies on Bayesian parameter inference, requiring a large number of evaluations of theoretical predictions such as the linear matter power spectrum. Although Boltzmann solvers provide accurate predictions, their computational cost represents a major limitation for cosmological analyses. This thesis presents the development and integration within CosmoBolognaLib of a neural-network emulator for the linear matter power spectrum. The approach exploits the evolution-mapping technique, which separates the dependence of the power spectrum into shape and evolution components. This allows a large fraction of the parameter dependence to be treated analytically or through physically motivated rescalings, while only the residual dependence is learned by the neural network, such that the emulator is trained only on the baryon and cold dark matter energy densities parameters. In particular, the emulator was trained on 80,000 power spectra spanning the baryon density in the range [0.03, 0.06] and cold dark matter density in the range [0.07, 0.70], with k sampled over [1.5×10^-4, 75] Mpc^-1. Its accuracy was first assessed on an independent test set of 20,000 spectra, obtaining residuals smaller than 0.1%. Its performance was then validated through complete Bayesian analyses of mock clustering measurements in standard and non standard cosmologies. In all cases, residuals remained below 0.1%, while posterior distributions were statistically consistent with those obtained using direct CAMB evaluations. The emulator reduced the execution time by approximately three orders of magnitude in all cases. The integration within CosmoBolognaLib enables existing inference pipelines to exploit these computational gains with minimal modifications and provides a flexible framework for future extensions to more complex cosmological models and observables.