Integrated perturbation theory for cosmological tensor fields. II. Loop corrections

Abstract

In the previous paper [arXiv:2210.10435], the nonlinear perturbation theory of cosmological density field is generalized to include the tensor-valued bias of astronomical objects, such as spins and shapes of galaxies and any other tensors of arbitrary ranks which are associated with objects that we can observe. We apply this newly developed method to explicitly calculate nonlinear power spectra and correlation functions both in real space and in redshift space. Multi-dimensional integrals that appear in loop corrections are reduced to combinations of one-dimensional Hankel transforms, thanks to the spherical basis of the formalism, and the final expressions are numerically evaluated in a very short time using an algorithm of the fast Fourier transforms such as \textsc{FFTLog}. As an illustrative example, numerical evaluations of loop corrections of the power spectrum and correlation function of the rank-2 tensor field are demonstrated with a simple model of tensor bias.

21 pages, 4 figures; this paper is the second of a series, the first one is arXiv:2210.10435, the third one is arXiv:2304.13304 and the fourth one is arXiv:2405.09038

References in corpus (11)

• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• Multi-Point Propagators in Cosmological Gravitational Instability
• Nonlinear Perturbation Theory Integrated with Nonlocal Bias, Redshift-space Distortions, and Primordial Non-Gaussianity
• Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields
• The Gravitational Shear--Intrinsic Ellipticity Correlation Functions of Luminous Red Galaxies in Observation and in the $\Lambda$CDM Model
• An EFT description of galaxy intrinsic alignments
• FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory
• FFT-PT: Reducing the two-loop large-scale structure power spectrum to low-dimensional radial integrals
• Integrated perturbation theory for cosmological tensor fields. I. Basic formulation
• Integrated perturbation theory for cosmological tensor fields. III. Projection effects
• Integrated perturbation theory for cosmological tensor fields. IV. Full-sky formulation

Cited by in corpus (5)

• Integrated perturbation theory for cosmological tensor fields. I. Basic formulation
• Integrated perturbation theory for cosmological tensor fields. III. Projection effects
• Integrated perturbation theory for cosmological tensor fields. IV. Full-sky formulation
• Cosmic Strings-induced CMB anisotropies in light of Weighted Morphology
• Degrees of Freedom of New General Relativity I: Type 2, Type 3, Type 5, and Type 8