Detecting the neutrino mass via the cross-correlation between matter tracers and the ISWRS effect?

TL;DR

This study assesses the feasibility of detecting the nonlinear Rees-Sciama (ISWRS) effect by cross-correlating current and future CMB experiments (SO, CMB-S4, CMB-HD, PICO) with ongoing LSS surveys (Euclid, LSST) in a νΛCDM framework. By modeling cross-correlations of ISWRS with gravitational-potential tracers—galaxy clustering, cosmic shear, and CMB-lensing potential—and incorporating massive neutrinos, the work identifies CMB-lensing (especially with CMB-HD) as the most promising avenue, capable of detections well above 5σ and potential discrimination among neutrino-mass scenarios; galaxy clustering can also deliver strong detections, particularly with optimal weighting and high-density LSST samples, whereas cosmic shear remains challenging due to nonlinear modelling uncertainties. The results underscore the crucial role of nonlinear power-spectrum modelling and delensing/foreground control in extracting ISWRS, with N-body simulations (e.g., DEMNUni) showing substantial improvements over analytic predictions for CS. While the forecasts confirm ISWRS detectability with upcoming facilities, they also suggest that groundbreaking new constraints on the total neutrino mass in the near term are unlikely, though these cross-correlations will provide valuable tests of νΛCDM and guide future modelling and survey design.

Abstract

This work explores the potential to detect the nonlinear Integrated Sachs Wolfe effect, namely the Rees-Sciama effect (ISWRS), by cross-correlating current and future Cosmic Microwave Background (CMB) experiments -- Simons Observatory, CMB-S4, CMB-HD, and PICO -- with ongoing Large Scale Structure (LSS) surveys, such as Euclid and the Vera Rubin Observatory (LSST). We model the cross-correlation of the ISWRS effect with gravitational potential tracers like galaxy clustering, cosmic shear, and CMB-lensing potential, to forecast results from these experiments. Our analysis also accounts for the presence of massive neutrinos to assess the feasibility of identifying the $ν$$Λ$CDM model and constraining the neutrino mass sum, M$ν$. Our findings indicate that the CMB-lensing potential reconstructed by CMB-HD is expected to provide the most promising results, achieving $\gtrsim$ 5$σ$ detections even under conservative assumptions for detector noise and foregrounds, thereby allowing differentiation between $ν$$Λ$CDM models. Galaxy clustering can also yield significant detections, whereas cosmic shear can provide valuable results only if non-linearities are accurately modelled, beyond the capabilities of currently available analytical approaches. These latter LSS probes do not provide strong constraining power on M$ν$. While our findings suggest that future CMB experiments and LSS surveys will enable the detection of the ISWRS effect, they do not imply significant prospects for imposing new constraints on neutrino masses in the near future.

Figures (13)

• Figure 1: Time evolution functions of the investigated fields. The solid red lines in the three panels represent the ISWRS response as a function of $z$ computed at a scale $k^{*} = (\ell^{*} + 1/2)/\chi(z)$, where $\ell^{*} = 5000$. (This specific scale has been choosen since it represents the range of nonlinear scales that mainly contribute to the cumulative $S/N$.) The left panel shows the window function of the Euclid photometric GC sample (dashed orange line), of the LSST "Gold" (dashed green line) and the LSST "Optimistic" GC samples (dashed blue line). The central panel represents the CS window function of the Euclid photometric survey (dotted purple line). Finally, the CMB lensing convergence window function is represented in the right panel (dot-dashed brown line).
• Figure 2: Analytical predictions for the cross-correlation between the ISWRS effect and GC, CS and CMBL, from left to right, computed for $\nu\Lambda$CDM models with five different values of the total neutrino mass: $M_{\nu} = 0.06 \text{ eV (orange)}, 0.12\text{ eV (green)}, 0.18\text{ eV (red)}, 0.24\text{ eV (purple)}, 0.30\text{ eV (brown)}$. Together with them, the results for the massless case have been reported (blue). As GC and CS probes, the Euclid photometric sample has been used EC20. The upper panels represent the absolute value of the three angular cross-power spectra. The lower ones show how the position of the characteristic sign inversion varies with the value of $M_{\nu}$.
• Figure 3: Comparison between the ISWRS angular auto-spectra extracted from DEMNUni simulations in the range $z=[0.02, 7]$ (solid lines) and those wrongly analytically computed (dashed lines), for three $M_{\nu}$ values: $0.0$ eV (blue), $0.17$ eV (orange), $0.30$ eV (green).
• Figure 4: The left panel represents the results of the cumulative signal-to-noise ratio (CUM. $S/N$) obtained using Equation \ref{['eq:snr_ideal']} with the $C_{\ell}^{\dot\Phi\dot\Phi}$ extracted from DEMNUni maps with $M_{\nu}$ = $0.0$ eV (blue), $0.17$ eV (orange), $0.30$ eV (green). The right panel shows the results for the identification of the $\nu\Lambda$CDM model with respect to the massless case, obtained using Equation \ref{['eq:mnu']}. We also add the result for the $\nu\Lambda$CDM cosmology with $M_{\nu}=0.53$ eV to show the actual increasing trend as the neutrino mass increases. Both panels present the results obtained with lensed (solid lines) and delensed (dotted lines) $C_{\ell}^{TT}$.
• Figure 5: CMB-lensing potential reconstruction noise levels for the four CMB experiments tested: SO (purple), CMB-S4 (blue), CMB-HD (orange), PICO (green). The Planck PR4 (red) has been reported as a reference. In black the theoretical CMB lensing potential for the Planck cosmology.