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.
