Effects of anisotropic stress in interacting dark matter – dark energy scenarios

We study a novel interacting dark energy $-$ dark matter scenario where the anisotropic stress of the large scale inhomogeneities is considered. The dark energy has a constant barotropic state parameter and the interaction model produces stable perturbations in the large scale of the universe. The resulting picture has been constrained using different astronomical data in a spatially flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe. We perform different combined analyses of the astronomical data to measure the effects of the anisotropic stress on the strength of the interaction and on other cosmological parameters as well. The analyses from several combined data show that a non-zero interaction in the dark sector is favored while a non-interaction scenario is still allowed within 68\% confidence-level (CL). The anisotropic stress measured from the observational data is also found to be small, and its zero value is permitted within the 68\% CL. The constraints on the dark energy equation of state, $w_x$, also point toward its `$-1$' value and hence the resulting picture looks like a non-interacting $w_x$CDM as well as $\Lambda$CDM cosmology. However, from the ratio of the CMB TT spectra, we see that the model has a deviation from the standard $\Lambda$CDM cosmology which is very hard to detect from the CMB TT spectra only. Although the deviation is not much significant, but from the present astronomical data, we cannot exclude such deviation. Overall, we find that the model is very close to the $\Lambda$CDM cosmology. Perhaps, a more accurate conclusion can be made with the next generation of surveys that are not so far. We also argue that the current tension on $H_0$ might be released for some combinations of the observational data. In fact, the allowance of $w_x$ in the phantom region is found to be more effective to release the tension on $H_0$.