Resumen:
In this study, we perform tests aiming to investigate the viability of alternative theories
to the Standard Cosmological Model by using two important tools: Gaussian Processes
and Markov Chain Monte Carlo. Using data from the background and perturbed Universe,
such as f(z), [f σ8](z), σ8(z), H(z), and DL(z), consistency tests were carried out by
measuring the structure growth index γ, alongside both qualitative and quantitative
comparisons between the ΛCDM model, extensions based on General Relativity, and
modified gravity models of the F(R) and F(Q) classes. We find that the ω0ωaCDM model,
with parameters obtained by the DESI collaboration, and the F(Q) model proved to be
competitive alternatives for describing cosmic evolution. However, in all cases, the ΛCDM
model remained the most favored by observations. Consequently, our results indicate
that any substitute model must possess small deviations from General Relativity and
successfully reproduce the cosmological phenomena of both the background and
perturbed Universe.
Palavras-chave: Cosmology; Large-scale structure of the Universe; Growth of cosmic structures;
Modified Gravity; Statistical analyses of cosmological datasets
