Geodesic curve-of-sight formulae for the cosmic microwave background: A unified treatment of redshift, time delay, and lensing

Ryo Saito, Atsushi Naruko, Takashi Hiramatsu, Misao Sasaki

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a perturbed geodesic (curve) instead of a background geodesic (line). In this approach, the separation of the gravitational and intrinsic effects are manifest. This approach can be considered as a generalization of the remapping approach of CMB lensing, where all the gravitational effects can be treated on the same footing.

Original languageEnglish
Article number051
JournalJournal of Cosmology and Astroparticle Physics
Volume2014
Issue number10
DOIs
Publication statusPublished - 2014 Oct 1

Keywords

  • CMBR theory
  • cosmological perturbation theory
  • integrated Sachs-Wolfe effect
  • non-gaussianity

ASJC Scopus subject areas

  • Astronomy and Astrophysics

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