The Aemulus Project. III. Emulation of the Galaxy Correlation Function

Abstract

Using the N-body simulations of the AEMULUS Project, we construct an emulator for the non-linear clustering of galaxies in real and redshift space. We construct our model of galaxy bias using the halo occupation framework, accounting for possible velocity bias. The model includes 15 parameters, including both cosmological and galaxy bias parameters. We demonstrate that our emulator achieves ∼ 1% precision at the scales of interest, 0.1 < r < 10 h −1 Mpc, and recovers the true cosmology when tested against independent simulations. Our primary parameters of interest are related to the growth rate of structure, f , and its degenerate combination f σ 8 . Using this emulator, we show that the constraining power on these parameters monotonically increases as smaller scales are included in the analysis, all the way down to 0.1 h −1 Mpc. For a BOSS-like survey, the constraints on f σ 8 from r < 30 h −1 Mpc scales alone are more than a factor of two tighter than those from the fiducial BOSS analysis of redshift-space clustering using perturbation theory at larger scales. The combination of real-and redshift-space clustering allows us to break the degeneracy between f and σ 8 , yielding a 9% constraint on f alone for a BOSS-like analysis. The current AEMULUS simulations limit this model to surveys of massive galaxies. Future simulations will allow this framework to be extended to all galaxy target types, including emission-line galaxies.

Cosmological Evidence Modelling: a new simulation-based approach to constrain cosmology on non-linear scales

“…First, it is important to realise that a surrogate model such as Gaussian process emulation cannot perfectly reproduce the full forward-modelling approach. In the case of Zhai et al (2019), it was shown that emulator inaccuracies are roughly of the same order of magnitude as the typical observational uncertainties of the data. This has two important implications.…”

“…Finally, the predictionsD are used as training points for an emulator, most commonly a Gaussian process emulator, to predictD for arbitrary points in the cosmology and galaxy-halo parameter space without the need to re-run expensive simulations. The most extensive example of such an emulator approach in the context of the small-scale clustering of galaxies is the work of Zhai et al (2019) (also see Kwan et al 2015;Nishimichi et al 2018;Wibking et al 2019b). In this study, the authors constructed an emulator for the redshift-space clustering of galaxies in the BOSS CMASS survey.…”

“…First, these emulator inaccuracies will degrade or possibly bias our posterior inference. In the work of Zhai et al (2019), typical cosmological constraints are degraded by a factor of ∼ 1.5 due to emulator noise. Secondly, the emulator accuracy will likely degrade further with increased dimensionality of C G. In principle, this could be mitigated by increasing the number of training points for the emulator.…”

“…Then, Z(D|C) is a R n C → R and D(C, G) a R n C +n G → R n D function. Typical numbers of (nD, nC, nG) are (42, 5, 12) (More et al 2015) or (37, 8, 7) (Zhai et al 2019). In principle, nD can be reduced in specific cases through principal component analysis (Nishimichi et al 2018) or by emulating fitting functions (McClintock et al 2019).…”

“…In other words, the uncertainty in the mean of the posterior of f σ8 due to the finite sampling of cosmology is of order 4 times smaller than the posterior uncertainty in f σ8 itself. Thus, our approach might be more precise than the emulation method which adds significant noise due to emulator errors (Zhai et al 2019).…”