Constraining Anisotropic Baryon Oscillations

TL;DR

This paper addresses the challenge of extracting independent measurements of the angular diameter distance $d_A(z)$ and the Hubble parameter $H(z)$ from baryon acoustic oscillations by exploiting anisotropic information in the two-dimensional power spectrum. It reframes the cosmology-induced rescaling into dilation and warping modes and shows that the monopole primarily constrains $d_A^2/H$, while the quadrupole carries a distinct sensitivity to $d_A H$ via warping. By fitting a warped quadrupole template to $P_2(k)$ and marginalizing over redshift-space distortions with a flexible bias function, the authors demonstrate a robust method to measure $d_A H$ and thus break the usual degeneracy, validated with N-body simulations. The result is a conservative but practical route to determine both $d_A$ and $H$ with high accuracy from BAO features, though with some degradation relative to ideal Fisher forecasts due to imperfect RSD knowledge.

Abstract

We present an analysis of anisotropic baryon acoustic oscillations and elucidate how a mis-estimation of the cosmology, which leads to incorrect values of the angular diameter distance, d_A, and Hubble parameter, H, manifest themselves in changes to the monopole and quadrupole power spectrum of biased tracers of the density field. Previous work has focused on the monopole power spectrum, and shown that the isotropic "dilation" combination d_A^2/H is robustly constrained by an overall shift in the scale of the baryon feature. We extend this by demonstrating that the quadrupole power spectrum is sensitive to an anisotropic "warping" mode d_A H, allowing one to break the degeneracy between d_A and H. We describe a method for measuring this warping, explicitly marginalizing over the form of redshift space distortions. We verify this method on N-body simulations and estimate that d_A H can be measured with a fractional accuracy of ~ 3/sqrt(V) % where the survey volume is estimated in (Gpc/h)^3.

Figures (2)

• Figure 1: The effect of warping on the $\ell=0$ and $2$ Legendre moments of the power spectrum, measured by averaging over the 40 PM simulations discussed in the text. To better highlight the baryon oscillations, we have divided out by the "no-wiggle" power spectrum of Nowiggle. The filled squares [black] are the unwarped power spectrum, the triangles [blue] are warped by 2%, the squares [red] by 5%, and circles [green] by 10%. The solid lines are the predictions for $\ell=2$ of the simple model in Eq. \ref{['eq:ltransform']}. The predictions for $\ell=0$ are equally accurate, although we don't plot them to avoid cluttering the plot.
• Figure 2: As in Fig. \ref{['fig:pkwarp']}, but for the redshift-space correlation function. Note that we assume $\xi(r,\mu) = \xi_{0} {\cal P}_{0} - \xi_{2} {\cal P}_{2} + ...$, so that the multipoles are mostly positive. Note that the feature in $\xi_2$ appears at larger separations than the comparable feature in $\xi_0$.