Testing one-loop galaxy bias: Joint analysis of power spectrum and bispectrum

We present a joint likelihood analysis of the real-space power spectrum and bispectrum measured from a variety of halo and galaxy mock catalogs. A novel aspect of this work is the inclusion of nonlinear triangle configurations for the bispectrum, made possible by a complete next-to-leading order (one-loop) description of galaxy bias, as is already common practice for the power spectrum. Based on the goodness of fit and the unbiasedness of the parameter posteriors, we accomplish a stringent validation of this model compared to the leading order (tree-level) bispectrum. Using measurement uncertainties that correspond to an effective survey volume of 6 (Gpc/h)(3), we determine that the one-loop corrections roughly double the applicable range of scales, from similar to 0.17 h/Mpc (tree level) to similar to 0.3 h/Mpc. This converts into a 1.5-2x improvement on constraints of the linear bias parameter at fixed cosmology, and a 1.5-2.4x shrinkage of uncertainties on the amplitude of fluctuations A(s), which clearly demonstrates the benefit of extracting information from nonlinear scales despite having to marginalize over a larger number of bias parameters. Besides, our precise measurements of galaxy bias parameters up to fourth order allow for thorough comparisons to coevolution relations, showing excellent agreement for all contributions generated by the nonlocal action of gravity. Using these relations in the likelihood analysis does not compromise the model validity and is crucial for obtaining the quoted improvements on A(s). We also analyzed the impact of higher-derivative and scale-dependent stochastic terms, finding that for a subset of our tracers the former can boost the performance of the tree-level model with constraints on A(s) that are only slightly degraded compared to the one-loop model.

Automated summary

In this study, a joint likelihood analysis of the real-space power spectrum and bispectrum measured from various halo and galaxy mock catalogs is presented, validating the stringentness of the one-loop correction model for galaxy bias compared to the tree-level bispectrum model. The results show that the one-loop corrections roughly double the applicable range of scales, leading to significant improvements in constraints on the linear bias parameter and the amplitude of fluctuations A(s).