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Nonlinear Perturbation Theory Integrated with Nonlocal Bias, Redshift-space Distortions, and Primordial Non-Gaussianity

The standard nonlinear perturbation theory of the gravitational instability is extended to incorporate the nonlocal bias, redshift-space distortions, and primordial non-Gaussianity. We show that local Eulerian bias is not generally compatible to local Lagrangian bias in nonlinear regime. The Eulerian and Lagrangian biases are nonlocally related order by order in the general perturbation theory. The relation between Eulerian and Lagrangian kernels of density perturbations with biasing are derived. The effects of primordial non-Gaussianity and redshift-space distortions are also incorporated in our general formalism, and diagrammatic methods are introduced. Vertex resummations of higher-order perturbations in the presence of bias are considered. Resummations of Lagrangian bias are shown to be essential to handle biasing schemes in a general framework.