What is the best way to measure baryonic acoustic oscillations?

TL;DR

This paper tackles how to extract robust BAO–driven cosmological constraints from galaxy clustering by clarifying that the peak of the two-point correlation function does not precisely mark the sound horizon, even in linear theory. Using 50 large-volume N-body simulations (L-BASICCII), it develops and tests a full-shape modelling approach for the correlation function that combines a dewiggled linear spectrum with non-linear corrections inspired by renormalized perturbation theory, along with treatments for redshift-space distortions and halo bias. The key result is that the dewiggled, RPT-informed correlation-function model yields essentially unbiased constraints on the dark energy equation of state and tighter distance measurements than power-spectrum–based BAO methods, with about 50% smaller errors in the distance scale and without systematic bias. The work demonstrates that future surveys should exploit the full shape of $\xi(r)$, validated by simulations, to achieve optimal BAO cosmology, and it highlights the continued importance of detailed modelling of non-linear evolution and bias in interpreting BAO signals.

Abstract

Oscillations in the baryon-photon fluid prior to recombination imprint different signatures on the power spectrum and correlation function of matter fluctuations. The measurement of these features using galaxy surveys has been proposed as means to determine the equation of state of the dark energy. The accuracy required to achieve competitive constraints demands an extremely good understanding of systematic effects which change the baryonic acoustic oscillation (BAO) imprint. We use 50 very large volume N-body simulations to investigate the BAO signature in the two-point correlation function. The location of the BAO bump does not correspond to the sound horizon scale at the level of accuracy required by future measurements, even before any dynamical or statistical effects are considered. Careful modelling of the correlation function is therefore required to extract the cosmological information encoded on large scales. We find that the correlation function is less affected by scale dependent effects than the power spectrum. We show that a model for the correlation function proposed by Crocce & Scoccimarro (2008), based on renormalised perturbation theory, gives an essentially unbiased measurement of the dark energy equation of state. This means that information from the large scale shape of the correlation function, in addition to the form of the BAO peak, can be used to provide robust constraints on cosmological parameters. The correlation function therefore provides a better constraint on the distance scale (~50% smaller errors with no systematic bias) than the more conservative approach required when using the power spectrum (i.e. which requires amplitude and long wavelength shape information to be discarded).

Figures (18)

• Figure 1: The correlation functions computed by Fourier transforming the power spectrum obtained using the EH98 formula for $P(k)$ for three cases: solid line - a fully consistent linear theory $P(k)$, dot-dashed line - a $P(k)$ with no Silk damping and with dominant velocity overshoot on all wavenumbers and dashed - a $P(k)$ with no Silk damping but a standard velocity overshoot. The arrows mark the location of the peak in the acoustic bump, defined as the local maximum. The shaded region indicates a 2% error on the sound horizon scale, which is shown by the central solid line.
• Figure 2: The true sound horizon, $s$ (solid line), and the position of the acoustic peak in the correlation function, $r_p$ (dot-dashed line), as a function of $\Omega_{\rm m}$ for a fixed value of $\Omega_{\rm b}=0.041$. The dotted lines indicate a 2% spread in the value of the sound horizon. The dashed line shows location of the acoustic bump when the EH98 formalism for $P(k)$ is replaced by a more accurate calculation made with CAMB (see text for details).
• Figure 3: The ratio of the power spectra obtained using the EH98 fitting formula (dot-dashed line) and CMBFAST (solid line) to the one obtained using CAMB.
• Figure 4: Upper panel: The correlation functions obtained by Fourier transforming the power spectra computed using the EH98 fitting formula (dot-dashed line), CAMB (solid line) and CMBFAST (dashed line). Lower panel: the residuals of the correlation functions obtained from the EH98 and CMBFAST power spectra with respect to that obtained using CAMB.
• Figure 5: Comparison of the correlation function of one realization in our ensemble estimated by direct pair counting (solid line) with the ones obtained by counts of cubical cells with grid sizes of $N_{\rm grid}=160$ (short-long dashed line), $N_{\rm grid}=240$ (dot-dashed line) and $N_{\rm grid}=360$ (dotted line) and the ones obtained using a dilute sample containing a fraction of 5% (dot-long dashed line), 20% (long dashed line) and 40% (dashed line) of the total sample (panel a). The deviations from the full (direct pair count) estimate can be better appreciated in panels (b) and (c), which show the difference $\xi_{\rm grid}(r)-\xi_{\rm full}(r)$ on a much expanded scale for the grid and for estimates derived from random samples of the dark matter particles respectively.