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We investigate the possibility of phantom crossing in the dark energy sector and the solution for the Hubble tension between early and late universe observations. We use robust combinations of different cosmological observations, namely the Cosmic Microwave Background (CMB), local measurement of Hubble constant (H0), Baryon Acoustic Oscillation (BAO) and SnIa for this purpose. For a combination of CMB+BAO data that is related to early universe physics, phantom crossing in the dark energy sector was confirmed at a 95% confidence level and we obtained the constraint H0=71.0−3.8+2.9 km/s/Mpc at a 68% confidence level, which is in perfect agreement with the local measurement by Riess et al. We show that constraints from different combinations 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 obtained the constraint H0=70.25±0.78 km/s/Mpc at a 68% confidence level and the phantom crossing happening at the scale factor am=0.851−0.031+0.048 at a 68% confidence level.

Almost in all interacting dark energy models present in the literature, the stability of the model becomes potentially sensitive to the dark energy equation of state parameter wx, and a singularity arises at 'wx = −1'. Thus, it becomes mandatory to test the stability of the model into two separate regions, namely, for quintessence and phantom. This essentially brings in a discontinuity into the parameters space for wx. Such discontinuity can be removed with some specific choices of the interaction or coupling function. In the present work we choose one particular coupling between dark matter and dark energy which can successfully remove such instability and we allow a dynamical dark energy equation of state parameter instead of the constant one. In particular, considering a dynamical dark energy equation of state with only one free parameter w0, representing the current value of the dark energy equation of state, we confront the interacting scenario with several observational datasets. The results show that the present cosmological data allow an interaction in the dark sector, in agreement with some latest claims by several authors, and additionally, a phantom behaviour in the dark energy equation of state is suggested at present. Moreover, for this case the tension on H0 is clearly released. As a final remark, we mention that according to the Bayesian analysis, Λ-cold dark matter (ΛCDM) is always favored over this interacting dark energy model. PACS numbers: 98.80.-k, 95.36.+x, 95.35.+d, 98.80.Es * Electronic address: d11102004@163.com † Electronic address: ankanju@iisermohali.ac.in ‡ Electronic address: eleonora.divalentino@manchester.ac.uk § Electronic address: supriya.maths@presiuniv.ac.in arXiv:1809.06883v3 [astro-ph.CO]