The Impact of the Fiducial Cosmology Assumption on BAO Cosmological Parameter Inference

TL;DR

This work assesses how assuming a fiducial cosmology in BAO analyses affects the inferred anisotropic BAO scales $\alpha_{\parallel}$ and $\alpha_{\perp}$. Using 40 Aemulus $w\mathrm{CDM}$ simulations and 4096 MD-PATCHY mocks, it probes 1600 combinations of true vs fiducial cosmologies across reconstruction and full pipeline steps. The main finding is that, for realistic cosmology differences, there is no significant systematic bias in $\alpha_{\parallel}$ and $\alpha_{\perp}$ ( sensitivities $<0.1\%$ ), though the uncertainties $\sigma_{\alpha_{\parallel}}$ and $\sigma_{\alpha_{\perp}}$ can increase by up to about $0.002$ and $0.001$ respectively when the fiducial model is far from truth. These results imply BAO inferences remain robust to fiducial-cosmology choices, with only modest degradation in precision, a reassuring conclusion for upcoming high-precision surveys such as DESI, Euclid, and WFIRST.

Abstract

Standard analysis pipelines for measurements of Baryon Acoustic Oscillations (BAO) in galaxy surveys make use of a fiducial cosmological model to guide the data compression required to transform from observed redshifts and angles to the measured angular and radial BAO peak positions. In order to remove any dependence on the fiducial cosmology from the results, all models compared to the data should mimic the compression and its dependence on the fiducial model. In practice, approximations are made when testing models: (1) There is assumed to be no residual dependence on the fiducial cosmology after reconstruction, (2) differences in the distance--redshift relationship are assumed to match a linear scaling, and (3) differences in clustering between true and fiducial models are assumed to be removed by the free parameters used to null the non-BAO signal. We test these approximations using the current standard measurement procedure with a set of halo catalogs from the {\sc Aemulus} suite of $N$-body simulations, which span a range of $w\mathrm{CDM}$ cosmological models. We focus on reconstruction of the primordial BAO and locating the BAO. For the range of $w\mathrm{CDM}$ cosmologies covered by the {\sc Aemulus} suite, we find no evidence for systematic errors in the measured BAO shift parameters $α_{\parallel}$ and $α_{\bot}$ to $< 0.1\%$. However, the measured errors $σ_{α_{\parallel}}$ and $σ_{α_{\bot}}$ show a notable absolute increase by up to $+0.001$ and $+0.002$ respectively in the case that the fiducial cosmology does not match the truth. These effects on the inferred BAO scale will be important given the precision of measurements expected from future surveys including DESI, Euclid, and WFIRST.

Figures (13)

• Figure 1: Comparison of the hypercube sampling in cosmological parameters against the likelihood contours of $w\mathrm{CDM}$ with the latest Planck 2018 + BOSS consensus 2017MNRAS.470.2617A2018arXiv180706209P.
• Figure 2: The correlation matrix built from the 4096 Patchy halo catalogues. The bottom left quadrant shows the correlation matrix for the monopole, upper right for the quadrupole and others show the cross-correlation between multipoles. The corresponding covariance matrix is scaled to allow for use with Aemulus simulations.
• Figure 3: Distributions of measured $\alpha_{\bot}$ and $\alpha_{\parallel}$ for the 1600 combinations of true box and assumed cosmologies used during reconstruction only. The distributions have $\alpha_{\bot}\pm\sigma_{\alpha_{\bot}} = 1.0029\pm0.010$ and $\alpha_{\parallel}\pm\sigma_{\alpha_{\parallel}} = 1.0052\pm0.024$ and scatter around 1 as expected. The clusters seen in the 2D distribution correspond to individual halo boxes and the sample variance in each sample.
• Figure 4: Distributions of measured $\Delta\alpha_{\bot}$ and $\Delta\alpha_{\parallel}$ for the 1600 combinations of true box and assumed cosmologies used during reconstruction only. These distributions have $\Delta\alpha_{\bot}\pm\sigma_{\Delta\alpha_{\bot}} = 0.00060\pm0.0029$ and $\Delta\alpha_{\parallel}\pm\sigma_{\Delta\alpha_{\parallel}} = 0.0013\pm0.0069$ and scatter around 0 as expected.
• Figure 5: The distribution of $\Delta\alpha_{\bot}$ plotted against the cosmological parameters which have been varied in the Aemulus simulations, for tests on reconstruction only. The 1600 scatter points have also been binned in 10 equally sized bins (black data points). The errorbars on these points correspond to the square root of the diagonal elements of the jack-knife re-sample generated covariance matrix. The solid lines with errors show a fit for a linear trend to the black data points. Comparison between the best fit linear trend and a zero-bias flat model show that there is mild evidence for a non-zero systematic bias at the $\Delta\alpha_{\bot}\sim 0.001$ level only for variations in $\Omega_{m}$ and $h$.