Interacting Dark Sectors in Anisotropic Universe: Observational
  Constraints and $H_{0}$ Tension
  The present study reveals observational constraints on the coupling between
dark components of anisotropic Bianchi type I universe. We assume interaction
between dark matter and dark energy and split the continuity equation with
inclusion of interaction term $\Gamma$. Two scenarios have been considered (i)
when coupling between dark components is constant and (ii) when it is a
function of redshift ($z$). Metropolis-Hasting algorithm has been used to
perform Monte Carlo Markov Chain (MCMC) analysis by using observational Hubble
data obtained from cosmic chronometric (CC) technique, cosmic microwave
background (CMB) baryon acoustic oscillation (BAO), Pantheon compilation of
Supernovae type Ia (SNIa), their joint combination and a gaussian prior on the
Hubble parameter $H_{0}$. It is obtained that the combination of all databases
plus $H_{0}$ prior marginalized over a present dark energy density gives
stringent constraints on the current value of coupling as $-0.001<\delta<0.041$
in constant coupling model and $-0.042<\delta<0.053$ in varying coupling model
at 68\% confident level. In general, for both models, we found
$\omega^{X}\approx -1$ and $\delta(\delta_{0})\approx 0$ which indicate that
still recent data favor uncoupled $\Lambda$CDM model. Our estimations show that
in constant coupling model $H_{0}=73.9^{+1.5}_{-0.95}$ which naturally solves
the Hubble tension problem. In other word, in constant coupling model, we did
not find any disagreement between our estimated $H_{0}$ and those reported by
Hubble space telescope (HST) and large scale structure (LSS) experiments.
