Where does non-Universality in Assembly Bias come from?

Constraints on local primordial non-Gaussianity (LPnG) obtained from galaxy power spectra are limited by the perfect degeneracy between the LPnG parameter $f_{\rm NL}$ and the bias parameter $b_{\phi}$ 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 $b_{\phi}$ and the galaxy bias $b_{g}$ is poorly understood and differs significantly from the universal mass function ansatz. In this paper, we investigate this non-universality in the context of dark-matter halos using the Separate Universe framework, focussing on dark-matter halos selected by mass and/or concentration. 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, independent of the spherical collapse picture of halo formation. We further propose an explanation for the observed non-universality in halos selected by concentration and corroborate it with $N$-body simulations in scale-free (EdS) and $\Lambda\text{CDM}$ cosmologies. In particular, we show that the relation between $b_{\phi}$ and halo bias $b_{h}$ for halos selected by concentration in matter-dominated cosmologies tends towards universality at the highest halo masses due to such halos gravitationally dominating their environment throughout their evolution. We also argue that concentration-selected halos of lower masses exhibit non-universality due to their mass accretion being significantly affected by the gravitational influence of neighbouring, more massive halos. Our results suggest that any non-universality in high redshift ($z\gtrsim 3$), high-bias objects observed by realistic galaxy surveys is entirely an artifact of the associated selection function.