Fitting cosmological data to the function $q(z)$ from GR Theory: Modified Chaplygin Gas

In the Friedmann cosmology the deceleration of the expansion $q$ plays a fundamental role. We derive the deceleration as a function of redshift $q(z)$ in two scenarios: $\Lambda$CDM model and modified Chaplygin gas ($MCG$) model. The function for the $MCG$ model is then fitted to the cosmological data in order to obtain the cosmological parameters that minimize $\chi^2$. We use the Fisher matrix to construct the covariance matrix of our parameters and reconstruct the q(z) function. We use Supernovae Ia, WMAP5 and BAO measurements to obtain the observational constraints. We determined the present acceleration as $q_0=-0.60 \pm 0.12$ for the $MCG$ model using the Constitution dataset of SNeIa and BAO, and $q_0=-0.63 \pm 0.17$ for the Union dataset and BAO. The transition redshift from deceleration to acceleration was found to be around $0.6$ for both datasets. We have also determined the dark energy parameter for the $MCG$ model: $\Omega_{X0}=0.834 \pm 0.028$ for the Constitution dataset and $\Omega_{X0}=0.854 \pm 0.036$ using the Union dataset.