Alleviating the Hubble Tension Using Coupled Dark Energy - Dark Matter Interaction
We investigate two interacting dark energy models, $ξ$CDM and $ξw$CDM, as potential means of alleviating the $H_0$ tension, using DESI DR2 BAO data along with the Planck 2018 CMB, Pantheon+ SNe Ia, and KiDS-1000/DES-Y3 weak lensing data. For the $ξ$CDM model, with a free coupling strength ($ξ$) and fixed dark energy equation-of-state ($w_0$), we find $H_0 = 71.59^{+1.69}_{-2.30}\mathrm{kms^{-1}Mpc^{-1}}$ from Planck-only data, tightening to $69.72^{+0.50}_{-0.41}\mathrm{kms^{-1}Mpc^{-1}}$ for the complete Planck+BAO+SN+WL dataset, reducing the tension from $\sim5.0σ$ to $\sim2.8σ$. In the $ξw$CDM model, with both $ξ$ and $w_0$ free, Planck-only data provide $H_0 = 72.46^{+4.05}_{-3.66}\mathrm{kms^{-1}Mpc^{-1}}$, while the full dataset yields $H_0 = 70.22^{+0.45}_{-0.40}\mathrm{kms^{-1}Mpc^{-1}}$, reducing the tension to $\sim2.5σ$, with phantom preference $w_0 = -1.116^{+0.043}_{-0.043}$ and negative coupling $ξ= -0.107^{+0.012}_{-0.023}$. With the convention $-ξH ρ_{de}$ >0, the negative coupling ($ξ< 0$) points to $Q > 0$, giving continuous energy transfer from dark energy to dark matter. This interaction modifies the evolution of the dark sector and the expansion history from early to late times, shifting the inferred $H_0$ to higher values. For the $ξw$CDM model, Planck+BAO+SN yields a substantial improvement in fit ($Δχ^2=-14.60$) and a strong AIC preference ($Δ\mathrm{AIC}=-10.60$), but $Δ\mathrm{BIC} = +0.30$ weakly prefers $Λ$CDM. Inclusion of WL data weakens the fit improvement ($Δχ^2 = -6.67$) yielding $Δ\mathrm{BIC} = +8.23$, a strong BIC preference for $Λ$CDM. This AIC/BIC discrepancy shows that the data favor the extra dark sector freedom, but not strongly enough to overcome the BIC penalty. These interacting models are therefore viable mechanisms for alleviating the $H_0$ tension.