Constraining cosmographic parameters with RSD data
$\Lambda$CD Mmodel; Cosmographic parameters; Matter densiti flutuations.
The Hubble constant $H_0$, the deceleration parameter $q_0$ and and the jerk $j_0$ are between some of most searched parameters in cosmology. These parameters gives information about the expansion rate, the acceleration and the acceleration rate of universe, respectively. In the final years of 20th century, supernova Ia distance measurements revealed that $q_0<0$ meaning that the universe is accelerating currently. The model which better explain the cosmic acceleration is the so-called $\Lambda$CDM model. However, the global estimate of $H_0$ (which use the $\Lambda$CDM as background model) and the local estimate of $H_0$ (which is model independent) presents a discrepancy of approximately $4\sigma$. This discrepancy puts problems on the $\Lambda$CDM model. In this scenario, the jerk parameter becomes an important piece for the validation of the $\Lambda$CDM model for which $j_0=1$. In this paper we perform a series expansion of $f\sigma_8$ and use the differential equation which provide the time evolution of $f\sigma_8$ as recurrence formula to write the series coefficients in terms of the kinematic parameters $q_0$ and $j_0$. From this process $f_0\sigma_{8,0}$, $q_0$, $j_0$, $\Omega_{{\rm m},0}$ and $\sigma_{8,0}$ emerges as free parameters. Then we use the $f\sigma_8$ data to constraining the free parameters. The Planck 2018 bounds on $\Omega_{{\rm m},0}$ and $\sigma_{8,0}$ are used to break the parameters degeneracy. We obtain that $j_0\neq1$ at $1\sigma$. Although the $\Lambda$CDM model is not the preferred model it can not be ruled out by the data used in our analysis.