Observational constraints on Myrzakulov gravity

We use data from Supernovae Pantheon sample, from baryonic acoustic oscillations, and from cosmic chronometers measurements of the Hubble parameter, alongside arguments from big bang nucleosynthesis, in order to extract constraints on Myrzakulov F(R,N) gravity. This is a connection-based theory belonging to the Riemann-Cartan subclass, that uses a specific but nonspecial connection, which then leads to extra degrees of freedom. Our analysis shows that both considered models lead to approximately 1 sigma compatibility in all cases. For the involved dimensionless parameter, we find that it is constrained to an interval around zero; however, the corresponding contours are slightly shifted toward positive values. Furthermore, we use the obtained parameter chains to reconstruct the corresponding Hubble function, as well as the dark energy equation-of-state parameter, as a function of redshift. As we show, model 1 is very close to Lambda-Cold Dark Matter (Lambda CDM) scenario, while model 2 resembles it at low redshifts; however, at earlier times, deviations are allowed. Finally, applying the Akaike Information Criterion, Bayesian Information Criterion, and combined Deviance Information Criterion criteria, we deduce that both models present a very efficient fitting behavior and are statistically equivalent with Lambda CDM cosmology, despite the fact that model 2 does not contain the latter as a limit.