Validating galaxy clustering models with Fixed & Paired and Matched-ICs simulations: application to Primordial Non-Gaussianities

Abstract

The Fix and Pair techniques were designed to generate simulations with reduced variance in the 2-point statistics by modifying the Initial Conditions (ICs). In this paper we show that this technique is also valid when the initial conditions have local non-Gaussianities (PNG), parametrised by 𝑓 NL , without biasing the 2-point statistics but reducing significantly their variance. We show how to quantitatively use these techniques to test the accuracy of galaxy/halo clustering models down to a much reduced uncertainty and we apply them to test the standard model for halo clustering in the presence of PNG. Additionally, we show that by Matching the stochastic part of the ICs for two different cosmologies (Gaussian and non-Gaussian) we obtain a large correlation between the (2-point) statistics that can explicitly be used to further reduce the uncertainty of the model testing. For our reference analysis (we obtain an uncertainty of 𝜎( 𝑓 NL ) = 60 with a standard simulation, whereas using Fixed [Fixed-Paired] initial conditions it reduces to 𝜎( 𝑓 NL ) = 12 [𝜎( 𝑓 NL ) = 12]. When also Matching the ICs we obtain 𝜎( 𝑓 NL ) = 18 for the standard case, and 𝜎( 𝑓 NL ) = 8 [𝜎( 𝑓 NL ) = 7] for Fixed [Fixed-Paired]. The combination of the Fix, Pair and Match techniques can be used in the context of PNG to create simulations with an effective volume incremented by a factor ∼ 70 at given computational resources.

Accurate predictions from small boxes: variance suppression via the Zel'dovich approximation

“…Another potential consideration is extending these techniques to the case of simulations with primordial non-Gaussianity (PNG). Matching phases between simulations with and without PNG has recently been demonstrated to be a powerful tool to isolate the effects of PNG in simulations with substantially less sample variance [85]. As biasing is well-understood in the presence of PNG [86], producing variance-reduced realizations of observables in the presence of PNG is well within the scope of the techniques we have laid out in this paper.…”

Can we actually constrain fNL using the scale-dependent bias effect? An illustration of the impact of galaxy bias uncertainties using the BOSS DR12 galaxy power spectrum

“…The sensitivity of these results to the assumed galaxy formation physics, as well as the connection between the simulated and the observed galaxy samples remains however currently unknown. Another interesting route could be to estimate the b φ (b 1 ) relation with the aid of semi-analytical models of galaxy formation tuned to match certain properties of galaxies in real surveys [86].…”

Can we actually constrain $f_{\rm NL}$ using the scale-dependent bias effect? An illustration of the impact of galaxy bias uncertainties using the BOSS DR12 galaxy power spectrum

“…The sensitivity of these results to the assumed galaxy formation physics, as well as the connection between the simulated and the observed galaxy samples remains however currently unknown. Another interesting route could be to estimate the b φ (b 1 ) relation with the aid of semi-analytical models of galaxy formation tuned to match certain properties of galaxies in real surveys [83]. Should future research directions like these succeed in providing trustworthy priors on the PNG bias relations, this will also offer us a chance to optimize galaxy clustering analyses to f nl constraints by targeting galaxy samples wiht the largest expected values for b φ .…”