Interpreting the Hubble tension with a cascade decaying dark matter sector

Hubble tension can be alleviated by altering either early- or late-time $\mathrm{\Lambda }$CDM. With only one of these effects introduced, early dark energy remains the only solution capable of reducing the tension to the $3\sigma$ level or below. In this work, we instead consider a modification of the dark matter sector that incorporates both the early- and late-time effects, with the goal of achieving the largest possible value of $H_0$ within this framework. As a realization of these two-fold effects, we study a cascade decaying dark matter model. By fitting the model to the latest datasets of Planck CMB+ DESI BAO+Pantheon (+SH0ES), we find that a 68$\mathrm{\%}$ CL value of $H_0=68.76\pm 0.35(69.05_{-0.27}^{+0.31})$ km s${}^{-1}$ Mpc${}^{-1}$ with $\mathrm{\Delta }{\chi }^2=+16.0(12.4)$, and larger value of $H_0$ can be obtained by adjusting parameter priors but with a cost of significantly increased value of $\mathrm{\Delta }{\chi }^2$. Our findings suggest that the Hubble tension cannot be reduced below the $3\sigma$ level, revising the earlier results on the tension level in the literature. For completeness, we show that the parameter regions favored by the cosmological datasets are compatible with complementary limits arising from the Big Bang Nucleosynthesis, neutrino flux, and structure formation.