A variable-slope smooth-k filter for modeling halo abundances with damped and oscillatory power spectra

Abstract We introduce a variable-slope smooth-k (VSMK) filter within the Press-Schechter formalism to model halo mass functions derived from damped and oscillatory matter power spectra. While the standard smooth-k approach successfully captures small-scale suppression effects, it intrinsically couples these to oscillatory features at intermediate scales. The VSMK filter generalizes this framework by allowing the effective logarithmic slope of the k-space window function to vary smoothly between two asymptotic regimes, thereby decoupling the small-scale suppression of halo abundances from the intermediate-scale oscillatory features characteristic of dark acoustic oscillations (DAO). We compare the analytic predictions obtained with the VSMK filter to N-body simulations for warm dark matter and ETHOS models with DAO, showing that a single parameter set reproduces both regimes simultaneously. The VSMK filter thus provides a unified and flexible analytic framework for modeling halo abundances in non-cold dark matter scenarios with damped and oscillatory power spectra.