On the universality of the halo mass function beyond ${\Lambda}$CDM cosmology

Theoretical frameworks based on Press-Schechter formalism and excursion set arguments suggest that the abundance of dark matter haloes exhibits universal behaviour when expressed in terms of peak height. If true, this implies that a single high-accuracy cosmological simulation could serve as a basis for constructing an emulator applicable to any other cosmology of interest. This tantalising possibility has inspired numerous studies over the years. However, in practice, different ways of defining haloes have led to mixed results concerning this issue. In this work, we utilise a suite of high-resolution cosmological $N$-body simulations, to revisit this question for friends-of-friends haloes under the flat, time-evolving $w$CDM model, with simple modifications of the primordial physics via variations in the scalar spectral index and its running. We construct a reference locus of $\nu f(\nu)$ from our fiducial ${\Lambda}$CDM simulation and compare it against measurements from alternative models. We find that deviations from the locus remain within $5 \%$ when varying each of the parameters within the ranges: ${w_0} = -1.0 \pm 0.1$, $w_a = 0\pm0.2$, $\Omega_{\rm DE} = 0.693\pm0.050$, $\omega_{\rm c} = 0.119\pm0.006$, $\omega_{\rm b} =0.0222\pm0.0011$, $A_{\rm s} = (2.15\pm0.22) \times {10^{-9}}$, $n_{\rm s} =0.961\pm0.048$, $\alpha_{\rm s}\ = 0\pm0.01$, for redshift $z < 7$.