Speaker
Description
Decaying dark matter (DDM) provides a well-motivated extension of $\Lambda$CDM, in which two-body decays -- characterized by a decay rate $\Gamma$ and velocity kick $v_k$ -- naturally suppress structure growth and lead to lower clustering amplitudes consistent with weak lensing measurements of $S_8$. Previous analyses combining Planck, BAO, and weak lensing data identified viable parameter space around $\Gamma^{-1} \sim 7$ Gyr and $v_k \sim 1250$ km/s. Extending these constraints with upcoming cluster abundance measurements from eROSITA, however, requires accurate theoretical predictions for the halo mass function in DDM cosmologies.
We show that the standard Press–Schechter formalism, even when supplied with the correct DDM linear power spectrum, systematically overpredicts the abundance of massive halos compared to DDM N-body simulations. This discrepancy arises from neglecting the distinct collapse physics of DDM, including the exponential decay of parent particles and mass loss from halos due to daughter particles receiving velocity kicks that exceed the escape velocity. We develop a spherical collapse framework that self-consistently incorporates these effects, yielding a mass-dependent critical density threshold $\delta_{\rm cr}(M)$ that increases for low-mass halos unable to retain kicked daughters. This leads to a suppression of low-mass halo abundances while recovering $\Lambda$CDM behavior at high masses. Comparing our theoretical predictions to simulations, we find that the DDM parameter space favored by Planck and weak lensing data produces substantially modified halo mass functions, indicating that eROSITA cluster counts should place significantly stronger constraints on decaying dark matter models.