Cosmological Spatial Curvature with the Alcock-Paczynski Effect

TL;DR

This paper introduces a model-independent method to measure the universe's spatial curvature using galaxy clustering data and the Alcock-Paczyński effect, avoiding reliance on standard candles or specific cosmological models.

Contribution

The authors develop a novel approach leveraging the Alcock-Paczyński effect to measure spatial curvature with minimal model assumptions, applicable to upcoming galaxy surveys.

Findings

Potential to measure curvature with $ riangle \,\Omega_{k0}=0.057$ at 1$\,\sigma$ using DESI-Euclid data.

Method is independent of galaxy bias, gravity theories, and pre-recombination physics.

Combines power-spectrum and bispectrum measurements for improved accuracy.

Abstract

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.