Exploring redshift-space distortions in large-scale structure

We explore and compare different ways large-scale structure observables in-space and real space can be connected. These include direct in Lagrangian space, moment expansions and two formulations of the model. We derive for the first time a Fourier space version of the model, which yields an algebraic relation between the real- and-space power spectra which can be compared to earlier, phenomenological. By considering the redshift-space 2-point function in both and Fourier space, we show how to generalize the Gaussian model to higher orders in a systematic and computationally tractable. We present a closed-form solution to the Zeldovich power spectrum in space and use this as a framework for exploring convergence properties different expansion approaches. While we use the Zeldovich approximation to these results, much of the formalism and many of the relations we hold beyond perturbation theory, and could be used with ingredients from N-body simulations or in other areas requiring decomposition of tensors times plane waves. We finish with a discussion of the-space bispectrum, bias and stochasticity and terms in Lagrangian theory up to 1-loop order.