Baryon Acoustic Oscillations in tomographic Angular Density and Redshift Fluctuations

TL;DR

This work develops a tomographic 2D approach to baryon acoustic oscillations by analyzing BAO signatures in the angular–redshift plane using two observables: ADF (galaxy angular density fluctuations) and ARF (galaxy angular redshift fluctuations). It formulates the projection framework, specifies Euclid-like and DESI-like survey configurations, and employs a Fisher matrix formalism to quantify information content from auto- and cross-spectra, including cross-shell correlations. The key finding is that BAO features encode the majority of cosmological and bias information, and that combining ADF and ARF yields order-of-magnitude improvements in constraints on $H_0$ and the CPL dark energy parameters $(w_0,w_a)$, especially when including neighboring shells and narrow shell widths $σ_z \leq 0.02$. This demonstrates the potential of BAO tomography in angular space as a robust complement to traditional 3D analyses for upcoming surveys, while highlighting practical considerations such as shell width, cross-shell convergence, and numerical stability in high-dimensional Fisher forecasts.

Abstract

In this work we examine the baryon acoustic oscillations (BAO) in 2D angular and redshift space $\{θ, Δz\}$, with $Δz$ denoting the redshift difference between two given angular shells. We thus work in the context of tomographic analyses of the large scale structure (LSS) where data are sliced in different redshift shells and constraints on Cosmology are extracted from the auto and cross-angular spectra of two different probes, namely the standard galaxy angular density fluctuations (ADF, or 2D clustering), and the galaxy angular redshift fluctuations (ARF). For these two observables we study by first time how the BAO peak arises in the $\{θ, Δz\}$ plane. Despite being a weak feature (particularly for $Δz \neq 0$), a Fisher forecast analysis shows that, a priori, most of the information on cosmological and galaxy bias parameters is carried by the BAO features in shell auto- and cross-angular power spectra. The same study shows that a joint probe analysis (ADF+ARF) increases the Fisher determinant associated to cosmological parameters such as $H_0$ or the Dark Energy Chevallier-Polarski-Linder (CPL) parameters $\{w_0,w_a\}$ by at least an order of magnitude. We also study how the Fisher information on cosmological and galaxy bias-related parameters behaves under different redshift shell configurations: including cross-correlations to neighbour shells extending up to $(Δz)^{\rm tot}\sim 0.6$ ($(Δz)^{\rm tot}\sim 0.4$) for ADF (ARF) is required for Fisher information to converge. At the same time, configurations using narrow shell widths ($σ_z \leq 0.02$) preserve the cosmological information associated to peculiar velocities and typically yield Fisher determinants that are about two orders of magnitudes larger than for wider shell ($σ_z>0.02$) configurations.

Figures (21)

• Figure 1: Redshift distributions adopted for the two models implemented (DESI-like model on the right panel, Euclid-like model on the left one).
• Figure 2: Correlation matrix between shells from (a) ADF, (b) ARF, and (c) ADF+ARF at $\ell=20$ from Eq. (\ref{['eq:cov_mat']}). Blue indicates positive correlation, white indicates no correlation, and red negative correlation.
• Figure 3: $w(\theta)$ for ARF (left panel) and ADF (right panel) for an Euclid-like survey. The colours from red to blue increase with $z_c$, $\Delta z = \sigma_z=0.038$.
• Figure 4: Comparing the relative height of the BAO peak over the zero-lag ($\theta=0$) peak in the auto-correlation function of shells centred at $z_c=0.61$ (left panel) and $z_c=0.91$ (right panel). In both cases, the ratio for the ARF cases (red lines) show a dramatic drop for $\sigma_z \ll (\Delta z)^{BAO}$ ($(\Delta z)^{BAO}\sim 0.045-0.055$ at those redshifts).
• Figure 5: Comparison of two-dimension correlation functions $\xi(\Delta z, \theta) \times \Delta z^{1.5}$ in ($\theta, \Delta z$) space, for ARF (left panel) and ADF (right panel).