Cosmological Parameters and Neutrino Masses from the Final Planck and Full-Shape BOSS Data

TL;DR

This paper tackles tightening cosmological parameter and neutrino-property constraints by combining Planck CMB data with the final BOSS galaxy power spectrum data using a new full-shape likelihood based on an improved perturbation-theory framework that includes IR resummation and counterterms. The neutrino sector is modeled with three degenerate masses and allows $N_{eff}$ to vary, enabling precise inference of $H_0$, $Ω_m$, $σ_8$, $M_{tot}$, and $N_{eff}$; results show $H_0=67.95^{+0.66}_{-0.52}$, $Ω_m=0.3079^{+0.0065}_{-0.0085}$, $σ_8=0.8087_{-0.0072}^{+0.012}$, and $M_{tot}<0.16$ eV (95% CL) with Planck+FS, and $N_{eff}=2.88±0.17$. Comparisons with Planck+BAO indicate the FS and BAO datasets carry similar informational power in this context, though their degeneracy directions differ when $N_{eff}$ is allowed to vary. Mock analyses of BAO damping reveal that the geometric information largely governs $H_0$, while broadband FS adds constraints on $ ext{shape}$-driven parameters; for Euclid-like surveys, FS is expected to dominate and yield even tighter neutrino-mass measurements. Overall, the study establishes a robust reference for current and future CMB+LSS analyses and highlights the pivotal role of full-shape information in precision cosmology.

Abstract

We present a joint analysis of the Planck cosmic microwave background (CMB) and Baryon Oscillation Spectroscopic Survey (BOSS) final data releases. A key novelty of our study is the use of a new full-shape (FS) likelihood for the redshift-space galaxy power spectrum of the BOSS data, based on an improved perturbation theory template. We show that the addition of the redshift space galaxy clustering measurements breaks degeneracies present in the CMB data alone and tightens constraints on cosmological parameters. Assuming the minimal $Λ$CDM cosmology with massive neutrinos, we find the following late-Universe parameters: the Hubble constant \mbox{$H_0=67.95^{+0.66}_{-0.52}$ km s$^{-1}$Mpc$^{-1}$}, the matter density fraction \mbox{$Ω_m=0.3079^{+0.0065}_{-0.0085}\,$}, the mass fluctuation amplitude \mbox{$σ_8=0.8087_{-0.0072}^{+0.012}\,$}, and an upper limit on the sum of neutrino masses \mbox{$M_{\text{tot}} <0.16\,$ eV} ($95\%$ CL).This can be contrasted with the Planck-only measurements: \mbox{$H_0=67.14_{-0.72}^{+1.3}$} km s$^{-1}$Mpc$^{-1}$, $Ω_m=0.3188^{+0.0091}_{-0.016}\,$, \mbox{$σ_8=0.8053_{-0.0091}^{+0.019}\,$}, and \mbox{$M_{\text{tot}} <0.26\,$ eV} ($95\%$ CL). Our bound on the sum of neutrino masses relaxes once the hierarchy-dependent priors from the oscillation experiments are imposed. The addition of the new FS likelihood also constrains the effective number of extra relativistic degrees of freedom, \mbox{$N_{\text{eff}}=2.88\pm 0.17$}. Our study shows that the current FS and the pure baryon acoustic oscillation data add a similar amount of information in combination with the Planck likelihood. We argue that this is just a coincidence given the BOSS volume and efficiency of the current reconstruction algorithms.In the era of future surveys FS will play a dominant role in cosmological parameter measurements.

Figures (3)

• Figure 1: Marginalized one-dimensional posterior distribution and two-dimensional probability contours (at the 68% and 95% CL) for the parameters of the $\Lambda$CDM model with varied neutrino masses. $N_{\text{eff}}$ is fixed to the standard model value $3.046$. $H_0$ is quoted in km/s/Mpc, $M_{\text{tot}}$ is quoted in eV.
• Figure 2: Marginalized one-dimensional posterior distribution and two-dimensional probability contours (at the 68% and 95% CL) for the parameters of the $\Lambda$CDM model with both varied neutrino masses and the effective number of relativistic degrees of freedom $N_{\text{eff}}$. $H_0$ is quoted in km/s/Mpc, $M_{\text{tot}}$ is quoted in eV.
• Figure 3: Marginalized one-dimensional posterior distribution and two-dimensional probability contours (at the 68% and 95% CL) for the parameters of simulated mock BOSS data. The shown are four cases corresponding to different amount of the BAO smoothing, see the main text for further details.