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

## TL;DR

This study evaluates how assumptions about the fiducial cosmology affect BAO measurements in galaxy surveys, finding minimal bias but increased uncertainties when the fiducial model differs from the true cosmology, which is relevant for future precise surveys.

## Contribution

The paper systematically tests the approximations used in BAO analysis pipelines across various cosmologies, quantifying their impact on measurement accuracy and uncertainties.

## Key findings

- No systematic bias in BAO shift parameters to <0.1%.
- Increased measurement errors up to +0.002 when fiducial cosmology mismatches true cosmology.
- Implications for future surveys like 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 $\alpha_{\parallel}$ and $\alpha_{\bot}$ to $< 0.1\%$. However, the measured errors $\sigma_{\alpha_{\parallel}}$ and $\sigma_{\alpha_{\bot}}$ 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.