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PreprintCC BY 4.0arXiv

Cosmological-perturbation equations from the total-angular-momentum formalism

  • Marc Kamionkowski
  • Robert R. Caldwell
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Abstract

We derive the equations for the linear evolution of cosmological perturbations using total-angular-momentum (TAM) waves. The cosmic microwave background temperature and polarization transfer functions are first derived as integral equations and from these the usual Boltzmann hierarchy of differential equations are then obtained for both scalar and tensor perturbations. We include the effects of isotropic cosmic birefringence and discuss anisotropic cosmic birefringence. We note a subtle effect of cosmic birefringence on temperature fluctuations. The TAM derivation of the equations provides physical insights to results obtained previously.

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Cite

BibTeXRIS
BibTeX
@misc{kamionkowski2026cosmologicalperturbation,
  title = {{Cosmological-perturbation equations from the total-angular-momentum formalism}},
  author = {Marc Kamionkowski and Robert R. Caldwell},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36000},
  eprint = {2609.36000},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36000},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Cosmological-perturbation equations from the total-angular-momentum formalism
AU  - Marc Kamionkowski
AU  - Robert R. Caldwell
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.36000
UR  - https://arxiv.org/abs/2609.36000
AB  - We derive the equations for the linear evolution of cosmological perturbations using total-angular-momentum (TAM) waves. The cosmic microwave background temperature and polarization transfer functions are first derived as integral equations and from these the usual Boltzmann hierarchy of differential equations are then obtained for both scalar and tensor perturbations. We include the effects of isotropic cosmic birefringence and discuss anisotropic cosmic birefringence. We note a subtle effect of cosmic birefringence on temperature fluctuations. The TAM derivation of the equations provides physical insights to results obtained previously.
ER  -