Toward a Complete Cosmological Analysis of Galaxy Clustering Measurements from Spectroscopic Redshift Surveys

The forthcoming generation of galaxy redshift surveys will sample the large-scale structure of the Universe over unprecedented volumes with high-density tracers. This advancement will make robust measurements of three-point clustering statistics not only possible, but necessary in order to exploit the surveys full potential to constrain cosmological models. My Ph.D. project is conceived specically for this improvement. Its main goal is the development of a software pipeline for the analysis of the joined galaxy power spectrum and bispectrum. In a rst stage, my collaborators and I investigate how several methodological choices can inuence inferences based on the bispectrum about galaxy bias and shot noise. We consider dark-matter halos, extracted from N-body simulations, of at least 1013Mb. While these are not representative of a realistic distribution of objects that is observed by redshift surveys, it is possible to extract a large number of synthetic catalogs of this type of objects from N-body simulations, and this still allows for comparison of perturbative models. We estimate the covariance matrix of the measurement errors by using 10,000 mock catalogues generated with the Pinocchio code, and then we t a series of theoretical models based on tree-level perturbation theory to the numerical data. We study how the model constraints are in uenced by the binning strategy for the bispectrum congurations and by the form of the likelihood function. We also use Bayesian model-selection techniques to single out the optimal theoretical description of our data. We nd that a three-parameter bias model at treelevel combined with Poissonian shot noise is necessary to model the halo bispectrum up to scales of kmax ß 0:09 hMpc−1, although tting formulae that relate the bias parameters can be helpful to reduce the freedom of the model without compromising accuracy. Our data clearly disfavour local Eulerian and local Lagrangian bias models and do not require corrections to Poissonian shot noise. We then approach our nal goal of a simultaneous analysis of the power spectrum and bispectrum in real space. We t measurements of power spectrum and bispectrum of dark-matter halos from the same set of N-body simulations, with a full covariance, including cross correlations between power spectrum and bispectrum, estimated by the same 10,000 mock catalogues. The theoretical models employed are perturbative predictions at tree-level for the bispectrum, and at one-loop level for the power spectrum, both based on the Eective Field Theory of the Large Scale Structure, including infrared resummation, that represent the state of the art in the analysis of galaxy clustering measurements. We focus on the constraints of bias and shot-noise parameters as a function of kmax, we study extensions of the parameter space and possible reductions through either phenomenological of physically-motivated bias relations; we explore the impact of dierent covariance approximations and binning eects on the theoretical predictions. We nd that a joint t of power spectrum and bispectrum with 4 bias parameters, one EFT counterterm and two shot-noise parameters gives a good description of our data up to kmax;P 0:21 hMpc−1 and kmax;B 0:09 hMpc−1. In this particular setup, we perform a simultaneous t of power spectrum and bispectrum including cosmological parameters, and consistently evaluating the theoretical predictions at each sampled point in parameter space. We recover the correct value of the cosmological parameters used to run the N-body simulations. We envision that the addition of the galaxy bispectrum to the galaxy power spectrum, being able to break degeneracies between the model parameters, will allow much tighter constraints on cosmological parameters in future analyses of actual data.