Stepped Partially Acoustic Dark Matter: Likelihood Analysis and Cosmological Tensions

We generalize the recently proposed Stepped Partially Acoustic Dark Matter (SPartAcous) model by including additional massless degrees of freedom in the dark radiation sector. We fit SPartAcous and its generalization against cosmological precision data from the cosmic microwave background, baryon acoustic oscillations, large-scale structure, supernovae type Ia, and Cepheid variables. We find that SPartAcous significantly reduces the $H_0$ tension but does not provide any meaningful improvement of the $S_8$ tension, while the generalized model succeeds in addressing both tensions, and provides a better fit than $\Lambda\mathrm{CDM}$ and other dark sector models proposed to address the same tensions. In the generalized model, $H_0$ can be raised to $71.4~\mathrm{km/s/Mpc}$ (the 95% upper limit) if the fitted data does not include the direct measurement from the SH0ES collaboration, and to $73.7~\mathrm{km/s/Mpc}$ (95% upper limit) if it does. A version of $\texttt{CLASS}$ that has been modified to analyze this model is publicly available at https://github.com/ManuelBuenAbad/class_spartacous