Cosmological Parameters from the BOSS Galaxy Power Spectrum

TL;DR

This paper performs a full-shape analysis of the BOSS DR12 galaxy power spectrum using a complete one-loop perturbation theory model with IR resummation for redshift-space distortions, inferred via MCMC without relying on Planck priors. The authors demonstrate that the power-spectrum shape and BAO features alone constrain late-Universe parameters like $H_0$, $Ω_m$, and $σ_8$ with precision comparable to Planck in ΛCDM, while neutrino masses remain weakly constrained by BOSS data alone. They quantify the information content into shape, geometry, and Alcock-Paczynski effects, showing that $D_V$ is the principal distance measure and that AP distortions are subdominant in ΛCDM but become relevant in extensions. The methodology, including a fast FFTLog-based perturbation theory implementation in CLASS, provides a scalable framework for future large-volume surveys and for exploring non-minimal cosmologies.

Abstract

We present cosmological parameter measurements from the publicly available Baryon Oscillation Spectroscopic Survey (BOSS) data on anisotropic galaxy clustering in Fourier space. Compared to previous studies, our analysis has two main novel features. First, we use a complete perturbation theory model that properly takes into account the non-linear effects of dark matter clustering, short-scale physics, galaxy bias, redshift-space distortions, and large-scale bulk flows. Second, we employ a Markov-Chain Monte-Carlo technique and consistently reevaluate the full power spectrum likelihood as we scan over different cosmologies. Our baseline analysis assumes minimal $Λ$CDM, varies the neutrino masses within a reasonably tight range, fixes the primordial power spectrum tilt, and uses the big bang nucleosynthesis prior on the physical baryon density $ω_b$. In this setup, we find the following late-Universe parameters: Hubble constant $H_0=(67.9\pm 1.1)$ km$\,$s$^{-1}$Mpc$^{-1}$, matter density fraction $Ω_m=0.295\pm 0.010$, and the mass fluctuation amplitude $σ_8=0.721\pm 0.043$. These parameters were measured directly from the BOSS data and independently of the Planck cosmic microwave background observations. Scanning over the power spectrum tilt or relaxing the other priors do not significantly alter our main conclusions. Finally, we discuss the information content of the BOSS power spectrum and show that it is dominated by the location of the baryon acoustic oscillations and the power spectrum shape. We argue that the contribution of the Alcock-Paczynski effect is marginal in $Λ$CDM, but becomes important for non-minimal cosmological models.

Figures (17)

• Figure 1: Left panel: The posterior distribution for the late-Universe parameters $H_0,\Omega_m$ and $\sigma_8$ obtained with priors on $\omega_b$ from Planck (gray contours) and BBN (blue contours). For comparison we also show the Planck 2018 posterior (red contours) for the same model (flat $\Lambda$CDM with massive neutrinos). Right panel: The monopole (black dots) and quadrupole (blue dots) power spectra moments of the BOSS data for high-z (upper panel) and low-z (lower panel) north galactic cap (NGC) samples, along with the best-fit theoretical model curves. The corresponding best-fit theoretical spectra are plotted in solid black and blue. $H_0$ is quoted in units [km/s/Mpc].
• Figure 2: The 2d posterior distribution for cosmological parameters extracted from the BOSS DR12 power spectrum likelihood. We show results for four independent samples of the BOSS data separately (left panel) and the combined likelihoods (right panel). In the latter case we also plot the posterior distribution for the parameters of a similar model ($\Lambda$CDM with massive neutrinos) measured from the final Planck 2018 CMB data. $H_0$ is quoted in units [km/s/Mpc].
• Figure 3: The posterior contours for the combined analysis assuming the Planck prior on $\omega_{b}$ (in gray), Planck priors on $\omega_{b}$ and $\omega_{cdm}$ (in light blue). For comparison also shown are the contours from the Planck CMB data for $\Lambda$CDM with massive neutrinos (in red). $H_0$ is quoted in units [km/s/Mpc].
• Figure 4: The effect of varying the physical baryon (left panel) and cold dark matter (right panel) densities on the shape of the linear matter power spectrum (at $z=0$). In the first case we adjust $\omega_{cdm}$ to keep $\omega_{m}$ fixed, while in the second case we put $\omega_b\to 0$ to illustrate shape modifications exclusively due to $\omega_{cdm}$. All other cosmological parameters are fixed to the Planck best-fit values Aghanim:2018eyx. The scale rage that dominates the constraints presented in this paper is [0.01, 0.25] $h$Mpc$^{-1}$.
• Figure 5: Upper left panel: the high-z NGC data along with the best fitting theory curves (solid lines) and a prediction of the test model with $\omega_{cdm}$ shifted by $3\sigma$ (dotted lines), for which we have refitted the other parameters. Upper right panel: the residuals between the two models $\Delta P_\ell = P_{\ell,\,{\rm shifted}}-P_{\ell,\,{\rm best-fit}}$ divided by the data errors. Lower panels: the residuals between the models $P_{\ell,\,{\rm best-fit}}$ (left panel), $P_{\ell,\,{\rm shifted}}$ (right panel) and the data.