Title:

  The integrated perturbation theory for cosmological tensor fields

  Abstact:

  Selected topics and results from my latest series of papers on the
  integrated perturbation theory for cosmological tensor fields
  (Papers I-IV) are presented. In these works, I have formulated a
  nonlinear perturbation theory for cosmological tensor fields in
  general. Cosmological tensor fields correspond to observable
  properties of astronomical objects, such as the spatial distribution
  of galaxy number density (scalar), angular momentum (pseudo-vector),
  and shapes (tensors of rank 2 and higher). To take advantage of
  rotational symmetry, the formalism is constructed based on the
  irreducible decomposition of tensors, identifying physical variables
  that remain invariant under coordinate system rotation. The
  projection effects onto the sky, which are more directly related to
  observations, are also taken into account. Symmetric properties in
  the projected tensor fields, such as rotation, parity, flipping, and
  complex conjugation, are made explicit. Extensions of the formalism
  from the distant-observer approximation to a full-sky formalism are
  also presented.

  References:

  T. Matsubara, PRD 110, id.063543 (2024) [arXiv:2210.10435] (Paper I)
  T. Matsubara, PRD 110, id.063544 (2024) [arXiv:2210.11085] (Paper II)
  T. Matsubara, PRD 110, id.063545 (2024) [arXiv:2304.13304] (Paper III)
  T. Matsubara, PRD 110, id.063546 (2024) [arXiv:2405.09038] (Paper IV)