Probing BAO studies with flat $\Lambda$CDM constraints

TL;DR

This paper critically examines the algorithms used for anisotropic BAO measurements, revealing their limitations at high redshifts and proposing flat b4bcdbcm constraints as a more reliable alternative for future cosmological studies.

Contribution

It identifies the deviations of current BAO algorithms from true solutions at high redshifts and advocates for flat b4bcdbcm constraints as a better approach.

Findings

BAO algorithms deviate from true solutions at high redshifts.

Transverse BAO measure b4bcdbcm is reliable in real space.

Isotropic BAO measure is affected by redshift distortion.

Abstract

One of the algorithms typically used for fitting anisotropic Baryon Acoustic Oscillations (BAO), $\alpha_{\perp}D_{M, \text{fid}}(z)/r_{d, \text{fid}}=D_{M}(z)/r_{d}$, provides an excellent fit as $z\Rightarrow 0$. Yet, at $ z_{\text{drag}} \simeq 1060$, $D_{M, \text{fid}}(1060)/r_{d, \text{fid}}\simeq D_{M}(1060)/r_{d}$. Since $\alpha_{\perp}$ does not change with increasing redshift, we conclude that the algorithms deviate from true solutions with increasing $z$. We investigate that departure through an assumption of a flat $\Lambda$CDM cosmology. At the relatively low redshifts at which isotropic BAO studies were performed, the divergence is smaller than study uncertainties. However, while the transverse measure, $\alpha_{\perp}$ provides a reliable value in real space, not corrupted by redshift distortion, the isotropic measure, $\alpha$, has a radial component, and is influenced by redshift distortion. That distortion recommends against the inclusion of isotropic studies in cosmological parameter evaluations. At the high redshifts of Ly$\alpha$ forest BAO studies, $z\sim$ 2.35, the deviations of the anisotropic BAO algorithms from the flat $\Lambda$CDM solutions give rise to markedly deceptive results. We replicate an example, in which those algorithms lead to a value of $\Omega_{m}$ which is more than 15 per cent lower than that of the flat $\Lambda$CDM cosmology computation. The BAO algorithms are inappropriate for the next generation of BAO studies. A flat $\Lambda$CDM analysis offers an alternative means of assessment.