Geometrical constraints on curvature from galaxy-lensing cross-correlations

TL;DR

This paper explores how galaxy-lensing cross-correlations can provide dark energy-independent constraints on the universe's curvature, significantly improving precision when combined with other cosmological probes.

Contribution

It introduces a comprehensive analysis of galaxy-lensing cross-correlations as a geometric probe for curvature, demonstrating their importance and potential to enhance constraints independently of dark energy assumptions.

Findings

Galaxy-lensing cross-correlations have high detection signal-to-noise ratios.

Adding galaxy-lensing data greatly improves curvature constraints.

Combining these methods yields a factor of 7 better constraint on curvature.

Abstract

Accurate constraints on curvature provide a powerful probe of inflation. However, curvature constraints based on specific assumptions of dark energy may lead to unreliable conclusions when used to test inflation models. To avoid this, it is important to obtain constraints that are independent on assumptions for dark energy. In this paper, we investigate such constraints on curvature from the geometrical probe constructed from galaxy-lensing cross-correlations. We study comprehensively the cross-correlations of galaxy with magnification, measured from type Ia supernovae's brightnesses ("$g\kappa^{\rm SN}$"), with shear ("$g\kappa^{\rm g}$"), and with CMB lensing ("$g\kappa^{\rm CMB}$"). We find for the LSST and Stage IV CMB surveys, "$g\kappa^{\rm SN}$" , "$g\kappa^{\rm g}$" and "$g\kappa^{\rm CMB}$" can be detected with signal-to-noise ratio $S/N=104,\ 2291,\ 1842$ respectively. When combined with supernovae Hubble diagram ("SN") to constrain curvature, we find galaxy-lensing cross-correlation becomes increasingly important with more degrees of freedom allowed in dark energy. Without any priors, we obtain error on $\Omega_K$ of $0.723$ from "SN + $g\kappa^{\rm SN}$", $0.0417$ from "SN + $g\kappa^{\rm g}$", and $0.04$ from "SN + $g\kappa^{\rm g}$ + $g\kappa^{\rm CMB}$" for the LSST and Stage IV CMB surveys. The last one is more competitive than a Stage IV BAO survey ("BAO"). When galaxy-lensing cross-correlations are added to the combined probe of "SN + BAO + CMB", where "CMB" stands for Planck measurement for the CMB acoustic scale, we obtain constraint on $\Omega_K$ of $0.0013$, which is a factor of 7 improvement from "SN + BAO + CMB". We study improvements in these results from increasing the high redshift extension of supernovae.