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 $(H_{0}=73.9^{+1.5}_{-0.95}, \delta=0.023^{+0.017}_{-0.024})$ which naturally leads to consistent value of the Hubble constant. This result is interesting because the previous works show that such a high value of Hubble constant requires the significant value of coupling parameter $\delta$. It has been also observed that in the constant coupling model, we do not find any disagreement between the estimated $H_{0}$ and those reported by Hubble space telescope (HST) and large scale structure (LSS) experiments.