Cosmological constraints from galaxy clustering in the presence of massive neutrinos

TL;DR

This work extends the clustering ratio observable, η_R(r)=ξ_R(r)/σ_R^2, to cosmologies with massive neutrinos and demonstrates its robustness to galaxy bias and redshift-space distortions on linear scales using DEMNUni simulations. The authors develop a likelihood framework to combine clustering-ratio measurements from SDSS with Planck CMB data, showing improved constraints on Ω_cdm h^2 and the dark-energy equation of state w, while neutrino mass constraints remain limited without smaller errors. They optimize the smoothing scale and correlation length to maximize information and define a neutrino-contrast metric to balance signal against theoretical uncertainties. Forecasts for a Euclid-like survey indicate substantial gains: ~14% tightening on M_ν and ~40% on Ω_cdm h^2 at 95% CL, underscoring the clustering ratio as a powerful, complementary probe for upcoming large-volume cosmological data. Overall, the clustering ratio proves to be a simple, unbiased, and effective tool for constraining key cosmological parameters in the presence of massive neutrinos, with significant potential when applied to future surveys.

Abstract

The clustering ratio is defined as the ratio between the correlation function and the variance of the smoothed overdensity field. In LCDM cosmologies not accounting for massive neutrinos, it has already been proved to be independent from bias and redshift space distortions on a range of linear scales. It therefore allows for a direct comparison of measurements (from galaxies in redshift space) to predictions (for matter in real space). In this paper we first extend the applicability of such properties of the clustering ratio to cosmologies that include massive neutrinos, by performing tests against simulated data. We then investigate the constraining power of the clustering ratio when cosmological parameters such as the total neutrino mass and the equation of state of dark energy are left free. We analyse the joint posterior distribution of the parameters that must satisfy, at the same time, the measurements of the galaxy clustering ratio in the SDSS DR12, and the angular power spectrum of temperature and polarization anisotropies of the CMB measured by the Planck satellite. We find the clustering ratio to be very sensitive to the CDM density parameter, but not very much so to the total neutrino mass. Lastly, we forecast the constraining power the clustering ratio will achieve with forthcoming surveys, predicting the amplitude of its errors in a Euclid-like galaxy survey. In this case, we find it is expected to improve the constraint at 95% level on the CDM density by 40% and on the total neutrino mass by 14%.

Figures (12)

• Figure 1: Correlation function of the Friend-of-Friends in the simulations with two different cosmologies. In the plot on the left there are the measurements in the $\Lambda$CDM cosmology, while in the plot on the right the $\Lambda$CDM$\nu$ simulation with $M_\nu=0.53$ eV. In both cases, left panel is at redshift $z=0.48551$ and right panel at $z=1.05352$. In the top panel we show the correlation function measured in the mass bins presented in Tab. \ref{['tab:mass-bins']} (points) compared to the theoretical smoothed matter correlation function (black solid line). In the bottom panel there is the FoF-matter bias, computed as $b=\sqrt{\xi^{FoF}_R(r)/\xi_R(r)}$. The linear bias in the simulation with massive neutrinos is larger than in the standard $\Lambda$CDM case, because, as neutrinos reduce clustering, massive haloes become rarer. We the bias values with a straight line between $R=16$ and $22~h^{-1}$Mpc. As the fit shows, the linear bias is compatible with being constant with scale.
• Figure 2: The clustering ratio of the Friend-of-Friends (FoF, left plot) and of the spherical overdensities with respect to the critical density (SO, right plot) computed in each mass bin at redshift $z=0.48551$ (left panel of each plot) and $z=1.05352$ (right panel) for all the neutrino masses. The smoothing radius is $R = 16 ~ h^{-1}$ Mpc and the correlation length is twice the smoothing radius. Points are measures in the simulations, while lines are the theoretical predictions. At $z=0.48551$ the agreement between measures and predictions is better than 3% in the bins with masses $< 30.43 h^{-1} \mathrm{M}_{\odot}$ (i.e. where the bias is $<2$), while in the bins with larger masses, corresponding to larger values of bias, the agreement is at 5% level. Errors are larger in the highest mass bin because it is more sparsely populated. At $z=1.05352$ the discrepancy between measures and predictions shows a specific dependence on the mass of the tracer. We consider this effect to be due a mass resolution effect in the simulation. Finally we point out that we find similar results for FoF and SO, meaning that the clustering ratio at these scales is insensitive to the linear bias irrespective of the mass tracer we choose.
• Figure 3: The clustering ratio smoothed on the scale $R$ and at correlation length $r=nR,~n=2$ as a function of the smoothing scale. We show in red the measures in the $\Lambda$CDM simulation and in blue the ones in the simulation with the highest neutrino mass, $M_\nu=0.53$ eV, which are the two extreme cases. Filled dots are measures in real space, while empty dots in redshift space. In the bottom panel the ratio between the clustering ratio in redhift space over the real space case is shown. Since on linear scales the monopole contribution coming from redshift-space distortions enhances the correlation function and the variance by the same multiplicative factor, we expect the clustering ratio to be unaffected. The ratio between redshift and real space measurements is, in fact, of order 1 with an accuracy better then 3%. This is even better confirmed in the case at redshift $z=1.055$ (right) because at higher redshift the matter growth is more linear.
• Figure 4: The effect of neutrinos on the clustering ratio compared to a $\Lambda$CDM cosmology. In the $(n,R)$ plane, we plot colour contours corresponding to $(\eta_R(r,\nu) - \eta_R(r,\Lambda \mathrm{CDM})/\sigma_{\eta}(\Lambda \mathrm{CDM)}$. As expected, the sensitivity to the neutrino total mass increases at small smoothing scales and correlation lengths (red regions).
• Figure 5: Discrepancy between the clustering ratio measured in the simulation and the theoretical prediction in the $(n,R)$ plane. Colours represent the quantity $(\eta_R(r) - \eta_{R}^{\rm th}(r)) / \sigma_{R}^(r)$, the blue regions being the ones with the best agreement with the predictions. Sufficiently large smoothing scales screen the effects of the nonlinear growth of perturbations, allowing us to exploit the clustering ratio as a cosmological probe. By smoothing our distribution on scales $R>19~h^{-1}$ Mpc we ensure an agreement with the model better then $\sim 1.5$ standard deviations.