A Variable-Slope Smooth-$k$ Filter for Modeling Halo Abundances with Damped and Oscillatory Power Spectra

TL;DR

This paper introduces a flexible variable-slope smooth-$k$ filter within the Press-Schechter formalism to accurately model halo mass functions in scenarios with damped and oscillatory matter power spectra, decoupling small-scale suppression from oscillatory features.

Contribution

The VSMK filter generalizes previous models by allowing the effective slope to vary smoothly, enabling a unified analytic approach for complex dark matter power spectra.

Findings

VSMK filter accurately reproduces halo abundances in simulations.

Single parameter set fits both damping and oscillatory regimes.

Provides a unified framework for non-cold dark matter models.

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. We compare the analytic predictions obtained with the VSMK filter to $N$-body simulations for warm dark matter and ETHOS-based models, 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.