Scale-dependent galaxy bias, CMB lensing-galaxy cross-correlation, and neutrino masses

TL;DR

The paper tackles the limitation that scale-dependent galaxy bias $b(k)$ imposes on extracting cosmological information from $P_{gg}(k)$, by jointly analyzing the CMB lensing–galaxy cross-correlation $C_\ell^{\rm \kappa g}$ and $P_{gg}(k)$ within a theoretically motivated bias framework $b_{ m cross}(k)=a+ck^2$ and $b_{ m auto}(k)=a+dk^2$. Using Planck 2015 CMB data, BOSS DR12 CMASS $P_{gg}(k)$, and DR11 CMASS $C_\ell^{\rm \kappa g}$, the authors constrain the bias parameters and, crucially, tighten the upper bound on the sum of neutrino masses to $M_\nu<0.19$ eV (95% CL) when all data are combined. The results demonstrate that scale-dependent bias modeling is essential for robust neutrino-mass constraints and show the method’s promise for future surveys with higher signal-to-noise in the cross-correlation, enabling substantial information recovery from mildly non-linear scales. The work lays out a path toward tomographic analyses and extension to non-linear regimes with perturbation-theory frameworks, which could yield even stronger constraints on small-scale growth and neutrino physics.

Abstract

One of the most powerful cosmological datasets when it comes to constraining neutrino masses is represented by galaxy power spectrum measurements, $P_{gg}(k)$. The constraining power of $P_{gg}(k)$ is however severely limited by uncertainties in the modeling of the scale-dependent galaxy bias $b(k)$. In this Letter we present a new method to constrain $b(k)$ by using the cross-correlation between the Cosmic Microwave Background (CMB) lensing signal and galaxy maps ($C_\ell^{\rm κg}$) using a simple but theoretically well-motivated parametrization for $b(k)$. We apply the method using $C_\ell^{\rm κg}$ measured by cross-correlating Planck lensing maps and the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 11 (DR11) CMASS galaxy sample, and $P_{gg}(k)$ measured from the BOSS DR12 CMASS sample. We detect a non-zero scale-dependence at moderate significance, which suggests that a proper modeling of $b(k)$ is necessary in order to reduce the impact of non-linearities and minimize the corresponding systematics. The accomplished increase in constraining power of $P_{gg}(k)$ is demonstrated by determining a 95% C.L. upper bound on the sum of the three active neutrino masses $M_ν$ of $M_ν<0.19\, {\rm eV}$. This limit represents a significant improvement over previous bounds with comparable datasets. Our method will prove especially powerful and important as future large-scale structure surveys will overlap more significantly with the CMB lensing kernel providing a large cross-correlation signal.

Figures (3)

• Figure 1: One-dimensional marginalized posterior for $M_{\nu}$ obtained with the baseline CMB dataset (CMB temperature and large-scale polarization anisotropy, black line), in combination with the $\boldsymbol{P_{gg}(k)}$ dataset (galaxy power spectrum from the DR12 CMASS sample, blue line), with the $\boldsymbol{C_\ell^{\rm \kappa g}\,}$ dataset (CMB lensing-galaxy overdensity cross-correlation angular power spectrum, green line), and with both $\boldsymbol{P_{gg}(k)}$ and $\boldsymbol{C_\ell^{\rm \kappa g}\,}$ (magenta line). We also show the posterior obtained in Vagnozzi:2017ovm for the CMB+$\boldsymbol{P_{gg}(k)}$ dataset with a scale-independent treatment of the bias (red line).
• Figure 2: 68% and 95% CL allowed regions in the combined two-dimensional planes for the parameters $M_{\nu}$, $a$ and $d$ [the bias parameter $d$ enters the modeling of $\boldsymbol{P_{gg}(k)}$ as this is an auto-correlation measurement, see Eqs. (\ref{['galaxy']}) and (\ref{['biasauto']})] together with their one-dimensional posterior probability distributions. We considered the combination of the CMB data with the $\boldsymbol{P_{gg}(k)}$ galaxy power spectrum data (blue contours), with the further addition of the $\boldsymbol{C_\ell^{\rm \kappa g}\,}$ CMB lensing-galaxy overdensity cross-correlation angular power spectrum (red contours). In order to compare these two combination of data, we do not show the parameter $c$ in the plot as it is not present in the auto-correlation parameterization [Eq. (\ref{['biasauto']})].
• Figure 3: One-dimensional marginalized posterior for $a$ (scale-independent bias parameter) obtained by combining the baseline CMB dataset, with the $P_{gg}(k)$ dataset and with the $C_{\ell}^{\kappa g}$ dataset used in this work. The red line shows the posterior obtained introducing the $k^2$-correction, while the black line illustrates the posterior obtained with a scale-independent treatment of the bias. The $k$ and $\ell$ range we choose are the same for both the cases considered.