Combining Full-Shape and BAO Analyses of Galaxy Power Spectra: A 1.6% CMB-independent constraint on H0

Abstract

We present cosmological constraints from a joint analysis of the pre- and post-reconstruction galaxy power spectrum multipoles from the final data release of the Baryon Oscillation Spectroscopic Survey (BOSS). Geometric constraints are obtained from the positions of BAO peaks in reconstructed spectra, analyzed in combination with the unreconstructed spectra in a full-shape (FS) likelihood using a joint covariance matrix, giving stronger parameter constraints than FS-only or BAO-only analyses. We introduce a new method for obtaining constraints from reconstructed spectra based on a correlated theoretical error, which is shown to be simple, robust, and applicable to any flavor of density-field reconstruction. Assuming $Λ$CDM with massive neutrinos, we analyze data from two redshift bins $z_\mathrm{eff}=0.38,0.61$ and obtain $1.6\%$ constraints on the Hubble constant $H_0$, using only a single prior on the current baryon density $ω_b$ from Big Bang Nucleosynthesis (BBN) and no knowledge of the power spectrum slope $n_s$. This gives $H_0 = 68.6\pm1.1\,\mathrm{km\,s}^{-1}\mathrm{Mpc}^{-1}$, with the inclusion of BAO data sharpening the measurement by $40\%$, representing one of the strongest current constraints on $H_0$ independent of cosmic microwave background data. Restricting to the best-fit slope $n_s$ from Planck (but without additional priors on the spectral shape), we obtain a $1\%$ $H_0$ measurement of $67.8\pm 0.7\,\mathrm{km\,s}^{-1}\mathrm{Mpc}^{-1}$. We find strong constraints on the cosmological parameters from a joint analysis of the FS, BAO, and Planck data. This sets new bounds on the sum of neutrino masses $\sum m_ν< 0.14\,\mathrm{eV}$ (at $95\%$ confidence) and the effective number of relativistic degrees of freedom $N_\mathrm{eff} = 2.90^{+0.15}_{-0.16}$, though contours are not appreciably narrowed by the inclusion of BAO data.

Figures (12)

• Figure 1: Power spectra used in this analysis, from both BOSS DR12 data, and MultiDark-Patchy mocks. For each separate chunk (at a different sky location and redshift bin), we show both the monopole ($\ell=0$, upper two spectra) and quadrupole ($\ell=2$, lower two spectra), before (darker colors) and after (lighter colors) density field reconstruction. Colored lines and shaded regions indicate the mean and $1\sigma$ variations between 999 mock catalogs in each chunk, with the data shown as black points. Errorbars indicate the square root of the covariance diagonal, estimated from the same set of mocks. We note that reconstruction sharpens the Fourier-space BAO wiggles, whilst slightly reducing the overall amplitude and removing most of the large-scale quadrupole power. Further note that the NGC data appears much smoother, due to the larger effective volumes of these regions.
• Figure 2: Posterior distribution of the Alcock-Paczynski (AP) parameters $\alpha_\parallel$, $\alpha_\perp$ (defined in Eq. \ref{['eq: AP-params']}) obtained from analysis of the high-z NGC BOSS DR12 power spectrum, after density-field reconstruction. Posterior samples are obtained by minimizing a likelihood consisting of a linear model with an additional theoretical error to account for the poorly-understood post-linear shape of the spectrum, as described in Sec. \ref{['subsec: recon-analysis']}. We show results from three choices of hyperparameters in the analysis; the fiducial choice (red), adopting a much narrower prior on the non-linear damping scale $\Sigma_\mathrm{NL}$ (blue) and inflating the theoretical error kernel (Eq. \ref{['eq: theoretical-err-kernel']}) by a factor of five. These contours were generated from $\sim 10^4$ posterior samples obtained from running 16 MCMC chains in parallel. We note negligible difference in the AP parameters from imposing a tight prior on $\Sigma_\mathrm{NL}$, with a slight bias obtained by inflating the theoretical error.
• Figure 3: Distribution of the best-fit AP parameters obtained from applying the BAO analysis method of Sec. \ref{['subsec: recon-analysis']} to 999 MultiDark-Patchy mock galaxy samples. For each mock, we plot the best-fit value obtained from an MCMC analysis which fits the corresponding power spectrum against a theoretical model and outputs a posterior distribution for $\{\alpha_\parallel, \alpha_\perp\}$. The dotted lines indicate the expected value for the mock cosmology (Sec. \ref{['subsec: mocks']}), with the black cross showing the average and $1\sigma$ deviation across all mocks. Note that the error bar is not normalized by the number of mocks, thus it represents the expected variation from a single mock. The red cross and dashed lines show the best-fit obtained (and its 68% and 95% confidence levels (CLs)) from analyzing the true BOSS data-set in this chunk (as tabulated in Tab. \ref{['tab: AP-results']}). A comparison of the posterior contour shapes for mocks and data is shown in Fig. \ref{['fig: ap-param-shape']}.
• Figure 4: Posterior distribution shapes for the AP parameter estimates shown in Fig. \ref{['fig: all-AP-params']}. We overplot the 68% and 95% CL contours from the BAO analysis of 999 mock galaxy samples in red, shifting the distribution to have zero mean. The corresponding posterior for the data in each patch is shown in blue. Note that the data contours are consistent with a random draw from the set of mock contours.
• Figure 5: Covariance of the unreconstructed monopole power and the AP parameters for the low-z NGC chunk, using data from 999 Patchy mocks. Black crosses (red circles) show the covariance of the parallel (perpendicular) parameter and we normalize by the unreconstructed power measurements and AP variance in each case. The blue line shows a rough estimate based on a simple model of the post-reconstruction wiggly power spectrum (Eq. \ref{['eq: cov-alpha-pk-estimate']}), and we note that this is capture the functional form well.