Publisher’s Note: Nonlinear clustering in models with primordial non-Gaussianity: The halo model approach [Phys. Rev. D83, 043526 (2011)]

Abstract

We develop the halo model of large-scale structure as an accurate tool for probing primordial non-Gaussianity (PNG). In this study we focus on understanding the matter clustering at several redshifts in the context of PNG that is a quadratic correction to the local Gaussian potential, characterized by the parameter fNL. In our formulation of the halo model we pay special attention to the effect of halo exclusion, and show that this can potentially solve the long standing problem of excess power on large scales in this model. The halo model depends on the mass function, clustering of halo centers and the density profiles. We test these ingredients using a large ensemble of highresolution Gaussian and non-Gaussian numerical simulations, covering fNL = {0, +100, −100}. In particular, we provide a first exploration of how halo density profiles change in the presence of PNG. We find that for fNL positive/negative high mass haloes have an increased/decreased core density, so being more/less concentrated than in the Gaussian case. We also examine the halo bias and show that, if the halo model is correct, then there is a small asymmetry in the scale-dependence of the bias on very large scales, which arises because the Gaussian bias must be renormalized. We show that the matter power spectrum is modified by ∼ 2.5% and ∼ 3.5% on scales k ∼ 1.0 h Mpc −1 at z = 0.0 and z = 1.0, respectively. Our halo model calculation reproduces the absolute amplitude to within 10% and the ratio of non-Gaussian to Gaussian spectra to within 1%. We also measure the matter correlation function and find similarly good levels of agreement between the halo model and the data. We anticipate that this modeling will be useful for constraining fNL from measurements of the shear correlation function in future weak lensing surveys such as Euclid.

Imprint of primordial non-Gaussianity on dark matter halo profiles

“…[23] and [26], to the simulations carried out in Ref. [27]. Although they simulated more massive halos than the one we have focused on, generally they found corrections to the density profile of order 2 − 5% for f NL = 100 (their Fig.…”

“…Indeed, there has been some work in this direction [27] which provided some fuel for the claim that non-Gaussianity does affect halo profiles. This work is complimentary: because we attack the problem semianalytically, we can probe the profile much closer to the center without any resolution issues.…”

Towards a self-consistent halo model for the nonlinear large-scale structure

“…(A4) and the low-k limit of the profile Eq. (9). Taking the derivative with respect to ln M s of this expression, it easy to verify that this result is independent of M s up to corrections of order (kR Ms ) 2 .…”

“…One could refer to the second, stochastic term, as 1-halo term, even though it involves a covariance between different halo masses. Alternatively, one could only refer to that part of the stochastic contribution that is proportional to δ D (ln M − ln M ) as 1-halo contribution, while the remainder of the stochastic part is considered a contribution to a modified 2-halo term (see also [9,41]). In any case, this separation is somewhat arbitrary and a matter of definition, as everything should be derived from the physical assumptions described in Sec.…”

“…Currently frequently employed incarnations of the halo model (e.g., [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]) have two major deficiencies: (i) they do not enforce the physical constraint of stress-energy conservation of matter; (ii) they are not guaranteed to recover exact perturbation theory (PT) results on large scales. The most widely known symptom of these deficiencies is the k-independent white noise contribution to the matter power spectrum P mm (k) of the 1-halo term on large scales.…”