Revisiting a non-parametric reconstruction of the deceleration parameter from combined background and the growth rate data

The cosmic deceleration parameter $q$ has been reconstructed in a non-parametric way using various combinations of recent observational datasets. The Pantheon compilation of the Supernova (SN) distance modulus data, the Cosmic Chronometer (CC) measurements of the Hubble parameter including the full systematics and the Baryon Acoustic Oscillation (BAO) data have been considered in this work. The redshift $z_t$, where the transition from a past decelerated to a late-time accelerated phase of evolution occurs, is estimated from the reconstructed $q$. The possible effect of a non-zero spatial curvature from the Planck 2020 estimate is checked. The outcome of including different $H_0$ measurements from recent Planck 2020 and Riess 2021 probes having a maximum discrepancy at the $4.2\sigma$ level, is investigated. Results indicate that the transition from a past decelerated phase to the late-time accelerated phase occurs within the redshift range $0.5<z<1$. For $z>1$, the reconstructed $q$ is observed to have a non-monotonic evolution in case of the combined CC and SN data. On introducing the BAO data, the reconstructed $q$ shows an oscillating behaviour for $z\gtrsim1$. To investigate the effect of matter perturbations, the growth rate data from the Redshift-Space Distortions (RSD) are utilized in reconstructing $q$. Using the $\mathcal{O}m(z)$ diagnostic, we draw inferences on the validity of $\Lambda$CDM as a consistency check. The $\Lambda$CDM model is well consistent and included at the 2$\sigma$ level in the domain of all the reconstructions.