Title:

The integrated perturbation theory for cosmological tensor fields

Abstract:

In order to extract maximal information about cosmology from the
large-scale structure of the Universe, one needs to use every bit of
signals that can be observed. Beyond the spatial distributions of
astronomical objects such as galaxies, the spatial correlations of
tensor fields, such as galaxy spins and shapes, are ones of promising
sources that we can access in the era of large surveys in near future.
The perturbation theory is a powerful tool to analytically describe
the behaviors and evolutions of correlation statistics for a given
cosmology. In this paper, we formulate a nonlinear perturbation theory
of tensor fields in general, based on the existing formulation of
integrated perturbation theory for the scalar-valued bias,
generalizing it to include the tensor-valued bias. In order to take
advantages of rotational symmetry, the formalism is constructed on the
basis of irreducible decomposition of tensors, identifying physical
variables which are invariant under the rotation of coordinates
system. Fundamental formulations and calculational techniques,
applications to some simple examples are presented.

References:

T. Matsubara, arxiv:2210.10435, arxiv:2210.11085
T. Matsubara, Phys. Rev. D 83, 083518 (2011)
T. Matsubara, Phys. Rev. D 90, 043537 (2014)
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