Cosmological Spatial Curvature with the Alcock-Paczynski Effect

We propose a methodology to measure the cosmological spatial curvature by employing the deviation from statistical isotropy due to the Alcock-Paczy\'nski effect of large scale galaxy clustering. This approach has a higher degree of model independence than most other proposed methods, being independent of calibration of standard candles, rulers, or clocks, of the power spectrum shape (and thus also of the pre-recombination physics), of the galaxy bias, of the theory of gravity, of the dark energy model and of the background cosmology in general. We find that a combined DESI-Euclid galaxy survey can achieve $\Delta \Omega_{k0}=0.057$ at 1$\sigma$ C.L. in the redshift range $z<2$ by combining power-spectrum and bispectrum measurements.