Simulations of Baryon Oscillations

TL;DR

This study addresses the challenge of using baryon acoustic oscillations as a precise cosmological ruler in galaxy surveys by leveraging high-resolution N-body simulations to create realistic mock catalogs with halo occupation modeling. It systematically tests multiple BAO models in real and redshift space, introduces a configuration-space band-power statistic, and employs robust fitting (including MCMC) to quantify biases in the inferred sound horizon and its sensitivity to non-linearities and galaxy physics. The results show that, for surveys covering several Gpc^3, the acoustic scale at z ≈ 1 can be measured at the ~1% level, with reconstruction and redshift-space modeling helping to mitigate degradation from non-linearity and bias. Overall, the work demonstrates the practical viability of BAO-based distance measurements for dark energy studies and informs the design of future large-volume surveys.

Abstract

The coupling of photons and baryons by Thomson scattering in the early universe imprints features in both the Cosmic Microwave Background (CMB) and matter power spectra. The former have been used to constrain a host of cosmological parameters, the latter have the potential to strongly constrain the expansion history of the universe and dark energy. Key to this program is the means to localize the primordial features in observations of galaxy spectra which necessarily involve galaxy bias, non-linear evolution and redshift space distortions. We present calculations, based on mock catalogs produced from high-resolution N-body simulations, which show the range of behaviors we might expect of galaxies in the real universe. We investigate physically motivated fitting forms which include the effects of non-linearity, galaxy bias and redshift space distortions and discuss methods for analysis of upcoming data. In agreement with earlier work, we find that a survey of several Gpc^3 would constrain the sound horizon at z~1 to about 1%.

Figures (14)

• Figure 1: (Upper) The cumulative mass function of halos from the 3 simulations at $z=1$. We define $M$ as $1.03\times$ the sum of the masses of the particles in the FoF group. The last point plotted in each case is the mass of the largest halo in the box. The solid line shows the fit of Ref. ST while the dotted line shows the results with $a=0.8$ and $p=0.25$ as discussed in the text. The horizontal dashed lines show the range of number densities of most interest for this work. (Lower) The ratio of the N-body results to the fit with $a=0.8$ and $p=0.25$.
• Figure 2: An estimate of the scale-dependence of the bias in configuration space. The different symbols are $\Delta\xi$ (see text) for different HOD models (from Table \ref{['tab:hod10']}) each divided by a constant bias to match near $100\,h^{-1}$Mpc. The degree to which the shapes match indicates how well each can be considered a constant times the dark matter correlation function. The lower panel shows the residuals from one of the models, taken as a template.
• Figure 3: A comparison of the different ways of computing $\xi(r)$ and $\Delta\xi(r)$ discussed in the text. In both panels open circles represent direct pair counting in the periodic box, filled triangles the Landy-Szalay estimator and open squares the Fourier transform method. For the $\Delta\xi(r)$ plot we also show the estimate of $\Delta\xi$ where $\bar{\xi}$ is obtained from counts in spheres as the stars. The different estimators differ in $\xi(r)$ at small $r$, so for the $\Delta\xi$ plot we have added an $r^{-1}$ term to make $r^2\Delta\xi=100$ at $r=100\,h^{-1}$Mpc for all of the lines. For $\xi(r)$ there is a noticeable shortfall in the power estimated by FFT methods at large $r$ which is largely absent for $\Delta\xi$.
• Figure 4: The fractional error in $\xi(r)$ (thin, upper) and $\Delta\xi(r)$ (thick, lower) computed in a smaller volume compared to the quantities in the full simulation. In each case we divided each simulation into $2^3$ (solid), $3^3$ (dashed) or $4^3$ (dotted) sub-cubes and computed $\xi(r)$ or $\Delta\xi(r)$ using the estimator of LanSza (see text). The curves display the deviation from the average computed with periodic boundary conditions in the full simulation.
• Figure 5: Contours of $\xi(r_p,\pi)$ (left) and $\Delta\xi(r_p,\pi)$ (right) for one of our $b\simeq 2$ catalogs. Contours are equally spaced in log, and dotted lines indicate negative values. Here $r_p$ measures separations across the line-of-sight and $\pi$ along it.