“DATA-DRIVEN COSMOLOGICAL RECONSTRUCTION USING GAUSSIAN PROCESSES AND MACHINE LEARNING”

Abstract

Modern cosmology provides a consistent description of the Universe on large scales, although fundamental questions, such as the nature of dark energy and the consistency among different cosmological estimates, remain open. Current surveys, such as DESI, pose new challenges to the $\Lambda$CDM model, while observations of the ages of cosmic objects offer a complementary way to probe the expansion history. In this context, machine learning techniques have gained increasing attention in the inference of cosmological observables. This thesis investigates their application to the reconstruction of such quantities, with emphasis on Symbolic Regression (SR). The analysis is based on the combined use of this approach and Gaussian Processes (GP), the latter employed as a non-parametric statistical method, allowing us to assess the consistency and robustness of the reconstructions. We use recent baryon acoustic oscillation data from DESI, combined with Type Ia supernovae, as well as galaxy age data from passively evolving systems.

In the context of dark energy, we reconstruct the equation-of-state parameter $w(z)$ directly from cosmological observables, aiming to investigate possible evidence for dynamical dark energy. This constitutes one of the first applications of symbolic regression to DESI data for this purpose. The reconstruction is initially performed using $D_H/r_d$ measurements, where $D_H$ is the Hubble distance and $r_d$ is the sound horizon at the drag epoch, and later refined using $D_M/r_d$, where $D_M$ is the transverse comoving distance, combined with supernova data.

Our results show that, given current uncertainties, there is no conclusive evidence for deviations from the $\Lambda$CDM model. The function $w(z)$ exhibits significant sensitivity to cosmological parameters, particularly $\Omega_m$ (matter density) and $r_d$, whose variations impact the inferred behavior. Nevertheless, the reconstructions remain consistent with $\Lambda$CDM at the $3\sigma$ level, with only marginal deviations in specific regions.

In the study of galaxy formation time, we reconstruct $t_f(z)$, defined as the cosmic time at which a given fraction of a galaxy's final stellar mass has formed, using two independent approaches based on different datasets. Both yield consistent results and indicate an evolution of $t_f(z)$ with redshift, particularly at low redshift. We also find that this estimate is weakly dependent on the assumed cosmological model, being mainly driven by uncertainties in cosmological parameters, especially $H_0$.