Exploring cosmological constraints on galaxy formation time

The Universe consists of a variety of objects that formed at different epochs, leading to variations in the formation time which represents the time elapsed from the onset of structure formation until the formation of a particular object. In this work, we present two approaches to reconstruct and constrain the galaxy formation time t f ( z ) using non-parametric reconstruction methods, such as Gaussian Processes (GP) and High-performance Symbolic Regression (SR). Our analysis uses age estimates of 32 old passive galaxies and the Pantheon+ type Ia supernova sample, and considers two different values of the Hubble constant H 0 from the SH0ES and Planck Collaborations. When adopting the ΛCDM model and the GP reconstructions, A direct comparison of the reconstructions shows that the GP-based implementations are mutually consistent across the redshift range considered. The SR reconstructions also show good agreement with the GP results and exhibit a compatible redshift evolution of t f ( z ), with full agreement at intermediate and high redshifts and only a mild deviation at very low redshifts. The results also show significant differences in the formation time from SH0ES and Planck values, highlighting the impact of the H 0 tension on the cosmological estimates of t f ( z ). Overall, this study suggests that galaxies have different evolutionary timescales and that t f is not constant, with noticeable variations at lower redshifts ( z ≲ 0.5).