  We discuss the discordance between the estimated values of the cosmological
parameters from Planck assuming the concordance $\Lambda$CDM model and
low-redshift measurements. In particular, we consider the Hubble constant
mismatch between Planck temperature constraint for the $\Lambda$CDM model and
the Riess et. al. local measurements as well as the discordance between the
estimated value of $S_8$ from Planck and some weak lensing surveys such as Kilo
Degree Survey (KiDS-450) and Dark Energy Survey (DES) observations. The
discordance can come from a wide range of non-standard cosmological or
astrophysical processes as well as from some particular systematics of the
observations. In this paper, without considering any particular astrophysical
process or extension to the standard model at the background level, we seek
solely to project the effect of these differences in the values of the key
cosmological parameters on to the shape of the primordial power spectrum (PPS).
In order to realise this goal, we uncover the shape of the PPS by implementing
the Modified Richardson-Lucy algorithm (MRL) that fits the Planck temperature
data as acceptably as the case of the standard model of cosmology, but with a
Hubble constant consistent with local measurements as well as improving the
consistency between the derived $S_8$ and $\sigma_8$ parameters with
estimations of the weak lensing surveys.
