Geometrical constraints on curvature from galaxy-lensing cross-correlations

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