Yismaw Wassie Ambelu, Amare Abebe Gidelew, Solomon Belay Tessema, Shambel Sahlu

The considerable difference between early and late universe measurements of the Hubble constant, called the Hubble tension, poses a potential challenge to the standard $Λ$CDM cosmological model. We examine an interacting dark matter-dark energy model, $Λ_s$CDM, characterized by a gauge-invariant coupling $Q = ξHρ_{\mathrm{de}}$ and an effective pressure dynamically induced within the dark matter fluid. Using the CLASS Boltzmann code modified in this work, we analyze both the background and perturbation observables and compute an extensive Markov Chain Monte Carlo analysis with the latest cosmological datasets, including observational Hubble parameter data, Planck 2018 CMB compressed likelihood, BAO (from DESI DR2), Pantheon+ Type Ia supernovae, and redshift-space distortion measurements. The model predicts $H_0 = 71.8_{-0.3}^{+0.4}\mathrm{kms^{-1}Mpc^{-1}}$, reducing the tension with the SH0ES local measurement from about $5σ$ in $Λ$CDM to $1.2σ$ in $Λ_s$CDM. In contrast to the early dark energy model, the resolution emerges from late-time modification of the expansion history induced by the energy transfer from dark matter to dark energy. Moreover, the model suppresses late-time structure growth, providing $σ_8 = 0.744 \pm 0.0185$, lying below the $Λ$CDM value and moves in the direction preferred by weak lensing surveys. Since the interaction term is suppressed at high redshift, the pre-recombination sound horizon departs by less than $1\%$ from its $Λ$CDM value, suggesting that the alleviation of the tension dominantly originates from the late-time expansion rather than early-universe effects. We conclude that $Λ_s$CDM constitutes a phenomenologically viable interacting dark sector framework that addresses key cosmological tensions while remaining consistent with current precision data. }