Early- and Late-Time Modifications to $\Lambda$CDM: Implications for the Hubble Tension

We investigate an extension of $\Lambda$CDM in which a fraction of cold Dark Matter (DM) decays into invisible dark radiation (DR) around the radiation-matter equality epoch, together with a non-standard dark energy (DE) equation of state characterized by $w_0$. The decaying DM component modifies the early expansion history and reduces the sound horizon at baryon drag, while the DE alters the expansion rate at the late times. A comprehensive analysis combining \texttt{Planck 2018+ACT DR6+DESI DR2+CMB lensing} datasets has been carried out to explore the viability of this framework in addressing the $H_0$ tension. This model yields a Hubble constant of $H_0 = 69.83 \pm 0.98~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, reducing the discrepancy with SH0ES measurement to ${\sim}2.2\sigma$ and local distance network measurement (H0DN) to ${\sim}2.9\sigma$. Further, considering \texttt{SH0ES} and \texttt{Pantheon+}, the inferred value of the Hubble constant becomes $H_0 = 70.20 \pm 0.66~\mathrm{km\,s^{-1}\,Mpc^{-1}}$. The Bayesian evidence suggests that this framework offers a fit to the relevant cosmological datasets at a statistically similar level as $\Lambda$CDM. It is observed that correlated early- and late-time modifications to the cosmological expansion history provide a more effective route to reducing the $H_0$ tension than either class of modification alone.