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 $F(R,T)$ 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 $\mathrm{\Lambda }$-Cold Dark Matter ($\mathrm{\Lambda }\mathrm{CDM}$) 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 $\mathrm{\Lambda }\mathrm{CDM}$ cosmology, despite the fact that model 2 does not contain the latter as a limit.

Figure 1

The $1\sigma$, $2\sigma$, and $3\sigma$ likelihood contours for model 1 of (2.22) and (2.23), for all possible two-dimensional subsets of the parameter space $({\mathrm{\Omega }}_{m0},h,\lambda ,\mathcal{M},r_d)$. Moreover, we present the mean parameter values within the $1\sigma$ area of the MCMC chain. We have performed a joint analysis of $\mathrm{CC}+\mathrm{SNIa}+\mathrm{BAO}$ data.

Figure 2

The $1\sigma$, $2\sigma$, and $3\sigma$ likelihood contours for model 2 of (2.31) and (2.32), for all possible two-dimensional subsets of the parameter space $({\mathrm{\Omega }}_{m0},h,\lambda ,\mathcal{M},r_d)$. Moreover, we present the mean parameter values within the $1\sigma$ area of the MCMC chain. We have performed a joint analysis of $\mathrm{CC}+\mathrm{SNIa}+\mathrm{BAO}$ data.

Figure 3

The reconstruction of the $H(z)/(z+1)$ as a function of the redshift for model 1, arisen from (2.20) and (2.22). We resampled the chains produced by emcee taking 6000 samples, and we plot all the obtained curves, alongside the curve corresponding to the best fit of the parameters (red curve).

Figure 4

The reconstruction of the $H(z)/(z+1)$ as a function of the redshift for model 2, arisen from (2.29) and (2.31). We resampled the chains produced by emcee taking 6000 samples, and we plot all the obtained curves, alongside the curve corresponding to the best fit of the parameters (red curve).

Figure 5

The reconstruction of the effective dark energy equation-of-state parameter $w_{de}(z)$ as a function of the redshift for model 1 given by (2.24). We resampled the chains produced by emcee taking 6000 samples, and we plot all the obtained $w_{de}(z)$ curves, alongside the curve corresponding to the best fit of the parameters (red curve).

Figure 6

The reconstruction of the effective dark energy equation-of-state parameter $w_{de}(z)$ as a function of the redshift for model 2 given by (2.33). We resampled the chains produced by emcee taking 6000 samples, and we plot all the obtained $w_{de}(z)$ curves, alongside the curve corresponding to the best fit of the parameters (red curve). The overpopulated area at the bottom corresponds to a peak within $1\sigma$ area; nevertheless, since we extract the median value of each parameter within $1\sigma$ as the best fit, the “best” $w_{de}(z)$ curve differs.