Cosmological implications of baryon acoustic oscillation (BAO) measurements

TL;DR

The paper investigates how baryon acoustic oscillation measurements, when combined with cosmic microwave background data and Type Ia supernovae, constrain the expansion history, curvature, and dark-energy models. By using high-precision BAO from BOSS (galaxy and Lyα forest) and a compressed CMB representation, the authors derive tight parameter constraints and test alternative cosmologies, including early dark energy, decaying dark matter, and extra relativistic species. A key result is the 1.7% determination of the Hubble constant, H0 = 67.3 ± 1.1 km s−1 Mpc−1, from an inverse distance ladder that relies on standard pre-recombination physics but minimal assumptions about dark energy or curvature. They also show that LyαF BAO data are in mild tension with ΛCDM predictions, while standard models remain broadly consistent with the data in terms of geometry, growth, and neutrino mass limits, highlighting the need for future high-redshift BAO and growth measurements to resolve remaining tensions.

Abstract

We derive constraints on cosmological parameters and tests of dark energy models from the combination of baryon acoustic oscillation (BAO) measurements with cosmic microwave background (CMB) and Type Ia supernova (SN) data. We take advantage of high-precision BAO measurements from galaxy clustering and the Ly-alpha forest (LyaF) in the BOSS survey of SDSS-III. BAO data alone yield a high confidence detection of dark energy, and in combination with the CMB angular acoustic scale they further imply a nearly flat universe. Combining BAO and SN data into an "inverse distance ladder" yields a 1.7% measurement of $H_0=67.3 \pm1.1$ km/s/Mpc. This measurement assumes standard pre-recombination physics but is insensitive to assumptions about dark energy or space curvature, so agreement with CMB-based estimates that assume a flat LCDM cosmology is an important corroboration of this minimal cosmological model. For open LCDM, our BAO+SN+CMB combination yields $Ω_m=0.301 \pm 0.008$ and curvature $Ω_k=-0.003 \pm 0.003$. When we allow more general forms of evolving dark energy, the BAO+SN+CMB parameter constraints remain consistent with flat LCDM. While the overall $χ^2$ of model fits is satisfactory, the LyaF BAO measurements are in moderate (2-2.5 sigma) tension with model predictions. Models with early dark energy that tracks the dominant energy component at high redshifts remain consistent with our constraints. Expansion history alone yields an upper limit of 0.56 eV on the summed mass of neutrino species, improving to 0.26 eV if we include Planck CMB lensing. Standard dark energy models constrained by our data predict a level of matter clustering that is high compared to most, but not all, observational estimates. (Abridged)

Figures (20)

• Figure 1: The BAO "Hubble diagram" from a world collection of detections. Blue, red, and green points show BAO measurements of $D_V/r_d$, $D_M/r_d$, and $z D_H/r_d$, respectively, from the sources indicated in the legend. These can be compared to the correspondingly colored lines, which represents predictions of the fiducial Planck $\Lambda$CDM model (with $\Omega_m=0.3183$, $h=0.6704$, see Section \ref{['sec:cmb']}). The scaling by $\sqrt{z}$ is arbitrary, chosen to compress the dynamic range sufficiently to make error bars visible on the plot. Filled points represent BOSS data, which yield the most precise BAO measurements at $z < 0.7$ and the only measurements at $z>2$. For visual clarity, the Ly$\alpha$ cross-correlation points have been shifted slightly in redshift; auto-correlation points are plotted at the correct effective redshift.
• Figure 2: BAO measurements and model predictions of $H(z)$ and $D_M(z)$ as a function of redshift, with physically informative scalings. The top panel shows $H(z)/(1+z)$, the proper velocity between two objects 1 comoving Mpc apart. The bottom panel shows $c\ln(1+z)/D_M(z)$, a scaling that matches a constant line $H(z)=(1+z) H_0$ in the top panel to the same constant line in the bottom panel for a flat universe. Filled circles and squares show the BOSS CMASS and LyaF measurements of $H(z)$ and $D_M(z)$, respectively; we show the LyaF-quasar cross-correlation as crosses to distinguish from the LyaF auto-correlation measurments. Filled triangles in the bottom panel show the BOSS LOWZ and MGS measurements of $D_V(z)$ converted to $D_M(z)$. Open squares show the value of $H_0 = 67.3\pm 1.1\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$ determined from the combination of BAO and SNIa data described in Section \ref{['sec:invdistladder']}. The grey swath in both panels is the prediction from the Planck $\Lambda$CDM cosmology including $1\sigma$ parameter errors; in the top panel, one can easily see the model transition from deceleration to acceleration at $z \approx 0.6$. The dashed line shows the $\Lambda$CDM prediction using the best-fit WMAP parameters, which has lower $\Omega_m h^2$. Dotted curves show models that match the best-fit Planck values of $\omega_{cb}$, $\omega_b$, and $D_M(1090)/r_d$ but have $\Omega_k=0.01$ (blue), $w=-0.7$ (green), or $w=-1.3$ (red). The $x$-axis is set to $\sqrt{1+z}$ both for display purposes and so that a pure matter universe ($\Omega_m=1$) appears as a decreasing straight line on the top panel.
• Figure 3: Constraints from BAO on the parameters of $o\Lambda$CDM models, treating the BAO scale as a redshift-independent standard ruler of unknown length. Green curves/contours in each panel show the combined constraints from galaxy and LyaF BAO, with no CMB information. Black curves/contours include the measurement of $D_M(1090)/r_d$ from the CMB acoustic scale, again with no assumption about the value of $r_d$ except that it is the same scale as the lower redshift measurements. This combination of BAO measurements yields precise constraints on $\Omega_\Lambda$ (top panel) and the dimensionless quantity $c/(H_0 r_d)$ (bottom panel), and it requires a low density ($\Omega_m \approx 0.29$), nearly flat universe (middle panel). Blue and red curves in the top and bottom panels show the result of combining the CMB BAO measurement with either the galaxy or LyaF BAO measurement separately. The dotted line in the middle panel marks $\Omega_m+\Omega_\Lambda=1$.
• Figure 4: Constraints on $\Omega_m$ and $h$ in a flat $\Lambda$CDM model from galaxy BAO (red), LyaF BAO (blue), and the combination of the two (green), using a BBN prior on $\omega_b$ and standard physics to compute the sound horizon $r_d$ but incorporating no CMB information. Contours are plotted at 68%, 95%, and 99.7% confidence (the interior white region of the green "donut" is 68%). Black contours show the entirely independent constraints on $\Omega_m$ and $h$ in $\Lambda$CDM from full Planck CMB chains.
• Figure 5: Determination of $H_0$ by the "inverse distance ladder" combining BAO absolute distance measurements and SNIa relative distance measurements, with CMB data used to calibrate the sound horizon scale $r_d$. The quantity $c\ln(1+z)/D_M(z)$ converges to $H_0$ at $z=0$. Filled circles show the four BAO measurements, normalized with $r_d = 147.49\,$Mpc; for the three lower redshift points, $D_V$ has been converted to $D_M$ assuming $\Lambda$CDM. Crosses show the SNIa measurements, with error bars representing diagonal elements of the covariance matrix. Because the absolute luminosity of SNIa is not known a priori, the SNIa points are free to shift vertically by a constant factor, which is chosen here to produce the best joint fit with the BAO data. The red square and error bar shows the value $H_0 = (67.3\pm 1.1)\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$ determined by the full inverse distance ladder procedure described in the text. The black curve shows the prediction for a $\Lambda$CDM model with $\Omega_m=0.3$ and the best-fit $H_0$, and green curves show ten PolyCDM models randomly selected from our MCMC chain that have $\Delta\chi^2 < 4$ relative to the best-fit PolyCDM model. This $H_0$ determination assumes standard pre-recombination physics to evaluate $r_d$. For non-standard energy backgrounds (e.g., extra relativistic species or early dark energy) the more general result is described by equation (\ref{['eqn:h0model']}).