Constraints on local primordial non-Gaussianity (LPnG) obtained from galaxy power spectra are limited by the perfect degeneracy between the LPnG parameter $f_{\mathrm{NL}}$ and the bias parameter $b_{\varphi }$, which encodes the response of galaxy clustering to a change in the amplitude of primordial curvature fluctuations. For galaxies observed by galaxy surveys, the relation between $b_{\varphi }$ and the galaxy bias $b_g$ is poorly understood and differs significantly from the universal mass function ansatz. In this paper, we investigate this nonuniversality in the context of dark-matter halos using the Separate Universe framework, focussing on dark-matter halos selected by mass and/or concentration as a test case—because halo concentration is the simplest example of a halo property correlated with nonuniversality. We show that the Separate Universe framework provides a natural explanation of the observed universality in the bias of dark-matter halos selected purely by their mass in terms of the response of the small-scale mass variance, ${\sigma }_8$, to ambient long-wavelength matter overdensity and to the amplitude of the primordial curvature fluctuations. Notably, the Separate Universe explanation for universality in this case is conceptually independent of the spherical collapse picture of halo formation. Furthermore, our Separate Universe arguments also show that halo clustering is in general nonuniversal whenever the halo abundance depends on properties of the small-scale matter density contrast whose responses to primordial curvature fluctuations and to a background long-wavelength matter overdensity differ from those of ${\sigma }_8$. Applying this insight from Separate Universe arguments to clustering of halos selected by mass and concentration, we propose an explanation for the observed nonuniversality in such halos and corroborate it with $N$-body simulations in scale-free (Einstein–de Sitter) and $\mathrm{\Lambda }$ cold dark matter cosmologies. We subsequently show that the clustering of concentration-selected halos in matter-dominated cosmologies tends toward universality at the highest halo masses because such halos gravitationally dominate their environment throughout their evolution. We also argue that concentration-selected halos of lower masses exhibit nonuniversality due to their mass accretion being significantly affected by the gravitational influence of neighboring, more massive halos. Our results also suggest that any nonuniversality in high redshift ($z\gtrsim 3$), high-bias objects observed by realistic galaxy surveys is likely just an artifact of the associated selection function.

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• Cosmological parameters
• Large scale structure of the Universe
• Massive compact halo objects