Modifying $\mathrm{\Lambda }$CDM dynamics via out-of-equilibrium axions: reconciling SH0ES and DESI $H_0$ values

We investigate late-Universe dynamics in which the dark matter component is described by axion particles. The proposed framework departs from the standard $\mathrm{\Lambda }$CDM paradigm due to a small fraction of axions driving the system away from thermal equilibrium. We analyze the evolution of the axion energy density using both a kinetic and a classical field approach, yielding an identical macroscopic evolution equation for the dark matter density. The resulting scenario modifies $\mathrm{\Lambda }$CDM dynamics in the late Universe (specifically at $z\lesssim 1$), while asymptotically recovering the standard baseline at earlier cosmic epochs. We compare the theoretical predictions of our formulation against a comprehensive suite of late-Universe datasets. Our statistical analysis reveals that when the SH0ES local calibration is included, the collisional axion model becomes significantly favored over $\mathrm{\Lambda }$CDM, yielding a best-fit Hubble constant of $H_0\simeq 73\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}$. Ultimately, this cosmological scenario successfully accommodates local distance-ladder measurements while maintaining excellent agreement with Baryon Acoustic Oscillation data from the DESI Collaboration.