Integrated perturbation theory and one-loop power spectra of biased tracers

Abstract

General and explicit predictions from the integrated perturbation theory (iPT) for power spectra and correlation functions of biased tracers are derived and presented in the one-loop approximation. The iPT is a general framework of the nonlinear perturbation theory of cosmological density fields in the presence of nonlocal bias, redshift-space distortions, and primordial non-Gaussianity. Analytic formulas of auto and cross power spectra of nonlocally biased tracers in both real and redshift spaces are derived and the results are comprehensively summarized. The main difference from previous formulas derived by the present author is to include the effects of generally nonlocal Lagrangian bias and primordial non-Gaussianity, and the derivation method of the new formula is fundamentally different from the previous one. Relations to recent work on improved methods of nonlinear perturbation theory in the literature are clarified and discussed.

Large-separation expansion of peak clustering in Gaussian random fields

“…The orthogonal expansion method of the Lagrangian bias in Refs. [18,30] is closely related to the formalism of integrated Perturbation Theory (iPT) [32][33][34][35]. In fact, the functional coefficients of the orthogonal expansion are the same as the renormalized bias functions in terms of iPT for Gaussian initial conditions.…”

Velocity bias and the nonlinear perturbation theory of peaks

“…The same type of seemingly linear term is also contained in a one-loop correction of iPT power spectrum. In the iPT, the normalized two-point propagator is given by [15] Γ (1)…”

“…For the diagrammatic rules of iPT, see Refs. [14,15]. The corresponding iPT diagram is denoted by a double square as shown in Fig.…”

Halo/galaxy bispectrum with equilateral-type primordial trispectrum

“…For a simple model of non-local halo bias proposed by Ref. [33,35], the renormalized bias function for halos with mass M is given by…”

“…[22], in this paper, we investigate the effect of these three equilateral-type primordial trispectra on the halo/galaxy bispectrum and see if we can get constraints on these trispectra from the future LSS observations independently from those from CMB. For this purpose, we adopt the integrated Perturbation Theory (iPT) [33] which enables us to connect the halo/galaxy clustering with the initial matter density field and incorporate the non-local biasing effect in a straightforward manner [18,[34][35][36][37]. Furthermore, it is worth mentioning that in iPT, we do not rely on the approximations like the peak-background split and the peak formalism.…”