Geometric Cosmology Models: Statistical Analysis with Observational Data

Although the standard cosmological model successfully describes most current observational data, it faces several theoretical and observational challenges that motivate the exploration of alternative frameworks. In this work, we investigate a class of geometric cosmology models (GC) obtained by adding an infinite tower of higher-order curvature invariants to the Einstein–Hilbert action. Focusing on an exponential ansatz for the characteristic function entering the modified Friedmann equations, we derive the late-time background evolution for three families of solutions within this framework, named as (i) GILA, (ii) GR-deformation, and (iii) non-GR contribution. These models are confronted with recent Cosmic Chronometer and Type Ia supernova data, as well as age estimates of the oldest globular clusters—a constraint frequently overlooked in the literature. The stiffness of the equations in certain regions of parameter space, together with technical difficulties arising from the inclusion of the globular cluster bound, motivates the development of a dedicated methodology as an alternative to standard Markov Chain Monte Carlo techniques. Our results show that two entire families of GC models (non-GR contribution and GR-deformation) are ruled out by the data, whereas some families within the GILA model can successfully account for all data sets. For these models, meaningful constraints on their free parameters can be derived from the statistical analysis. Nevertheless, model comparison criteria reveal a preference in the data for ΛCDM over the GILA models examined here. Although none of the proposed models provides a preferred alternative to ΛCDM given the specific characteristic function considered here, this work establishes a clear methodology for testing alternative cosmological models, including the globular cluster constraint, and indicates the way for future research of GILA models with alternative choices of the characteristic function.