Geometric and dynamic distortions in anisotropic galaxy clustering

Abstract

We examine the signature of dynamic (redshift-space) distortions and geometric distortions (including the Alcock-Paczynski effect) in the context of the galaxy power spectrum measured in upcoming galaxy redshift surveys. Information comes from both the baryon acoustic oscillation (BAO) feature and the broadband power spectrum shape. Accurate modeling is required to extract this information without introducing systematic biases in the result. We consider an analytic model for the power spectrum of dark matter halos in redshift space, based on the distribution function expansion, and compare with halo clustering measured in N-body simulations. We forecast that the distribution function model is sufficiently accurate to allow the inclusion of broadband information on scales down to k~0.2 h/Mpc, with somewhat better accuracy for higher bias halos. Compared with a BAO-only analysis with reconstruction, including broadband shape information can improve unbiased constraints on distance measures H(z) and D_A(z) by ~30% and 20%, respectively, for a galaxy sample similar to the DESI luminous red galaxies. The gains in precision are larger in the absence of BAO reconstruction. Furthermore, including broadband shape information allows the measurement of structure growth, through redshift-space distortions. For the same galaxy sample, the distribution function model is able to constrain f*sigma_8 to ~2%, when simultaneously fitting for H(z) and D_A(z). We discuss techniques to optimize the analysis of the power spectrum, including removing modes near the line-of-sight that are particularly challenging to model, and whether these approaches can improve parameter constraints. We find that such techniques are unlikely to significantly improve constraints on geometry, although they may allow higher precision measurements of redshift-space distortions.