Dark Energy with Phantom Crossing and the $H_0$ tension
  We investigate the possibility of phantom crossing in the dark energy sector
and solution for the Hubble tension between early and late universe
observations. We use robust combinations of different cosmological
observations, namely the CMB, local measurement of Hubble constant ($H_0$), BAO
and SnIa for this purpose. For a combination of CMB+BAO data which is related
to early Universe physics, phantom crossing in the dark energy sector is
confirmed at $95$\% confidence level and we obtain the constraint
$H_0=71.0^{+2.9}_{-3.8}$ km/s/Mpc at 68\% confidence level which is in perfect
agreement with the local measurement by Riess et al. We show that constraints
from different combination of data are consistent with each other and all of
them are consistent with phantom crossing in the dark energy sector. For the
combination of all data considered, we obtain the constraint $H_0=70.25\pm
0.78$ km/s/Mpc at 68\% confidence level and the phantom crossing happening at
the scale factor $a_m=0.851^{+0.048}_{-0.031}$ at 68\% confidence level.
