Geometrical constraints on curvature from galaxy-lensing cross-correlations

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 ("$g{\kappa }^{\mathrm{SN}}$"), with shear ("$g{\kappa }^{\mathrm{g}}$"), and with CMB lensing ("$g{\kappa }^{\mathrm{CMB}}$"). We find for the LSST and Stage IV CMB surveys, "$g{\kappa }^{\mathrm{SN}}$" , "$g{\kappa }^{\mathrm{g}}$" and "$g{\kappa }^{\mathrm{CMB}}$" 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 + $g{\kappa }^{\mathrm{SN}}$", $0.0417$ from "SN + $g{\kappa }^{\mathrm{g}}$", and $0.04$ from "SN + $g{\kappa }^{\mathrm{g}}$ + $g{\kappa }^{\mathrm{CMB}}$" 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.

13 pages, 4 figures, 3 tables, minor modifications reflect PRD accepted version

References in corpus (8)

• Dark Energy and the Accelerating Universe
• Planck evidence for a closed Universe and a possible crisis for cosmology
• A Parameterized Post-Friedmann Framework for Modified Gravity
• Crossing the Phantom Divide with Parameterized Post-Friedmann Dark Energy
• Dynamical Dark Energy or Simply Cosmic Curvature?
• Constraining Dark Energy by Combining Cluster Counts and Shear-Shear Correlations in a Weak Lensing Survey
• Measuring weak lensing correlations of Type Ia Supernovae
• Effect of lensing magnification on type Ia supernova cosmology

Cited by in corpus (2)

• Role of Spatial Curvature in a Dark Energy Interacting Model
• Effect of peculiar velocities of inhomogeneities on the shape of gravitational potential in spatially curved universe