Investigating the Hubble tension and σ ₈ discrepancy in f(Q) cosmology

Abstract In this study, we incorporated a three-parameter family, of the metric incompatible modification of standard general relativity ω models into the Boltzmann code MGCLASS at both the background and perturbation levels, in order to conduct a Bayesian study employing probes that include the cosmic microwave background (CMB), baryon acoustic oscillations (BAO), weak lensing (WL), alone or its correlation with galaxy clustering (3×2pt) and growth measurements f σ 8 , for each submodel. Our analysis focused on the impact of the Hubble tension in H 0 and the discrepancy in σ 8 resulting from the inclusion of our model's parameters, namely M , α and β . We find that none of the sub models, considered alone or combined, were able of alleviating the Hubble tension with only reducing it to 3 σ in the least constraining, highest degree of freedom case while we found that the σ 8 discrepancy, already strongly mitigated on WL linear scales, especially when we let all our model's parameters as free, appears again when considering the more constraining 3×2pt probe. Among the parameters considered, we found that β , acting in scaling both the gravitational and the Hubble parameter, had the most impact in reducing the discrepancy, with data preferring far from ΛCDM alike values, before the combination with fσ 8 constrain it back to its general relativity values.