Cosmology with anisotropic galaxy clustering from the combination of power spectrum and bispectrum

The apparent anisotropies of the galaxy clustering in observable redshift space provide a unique opportunity to simultaneously probe cosmic expansion and gravity on cosmological scales via the Alcock-Paczynski effect and redshift-space distortions. While the improved theoretical models have been proposed and developed to describe the apparent anisotropic clustering at weakly non-linear scales, the applicability of these models is still limited in the presence of the non-perturbative smearing effect caused by the randomness of the relative velocities. Although the cosmological constraint from the anisotropic clustering will be improved with a more elaborate theoretical model, here we consider an alternative approach using the statistical power of both the power spectrum and bispectrum at large scales. Based on the Fisher matrix analysis, we estimate the benefit of combining the power spectrum and bispectrum, finding that for the future spectroscopy survey DESI (Dark Energy Spectroscopy Instrument), the constraints on the cosmic expansion and growth of structure will be improved by a factor of two. This approach compensates for the loss of constraining power, using the power spectrum alone, due to the randomness of the relative velocities