2014/01/22 by S.-C. Su, S. -C. Su, Eugene A. Lim · 2 citations
Physics and Astronomy · #Anisotropy #Astrophysics #Boltzmann constant #Boltzmann equation #Cosmic microwave background #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #Formalism (music) #Galaxies: Formation, Evolution, Phenomena #Galaxy #Gravitational lensing formalism #Physics #Planck #Quantum mechanics #Redshift #Spectral density #Statistical physics #Weak gravitational lensing #astro-ph.CO #gr-qc #msc:83F05
paper · pdf · doi:10.1103/physrevd.89.123006
published as Phys. Rev. D 89, 123006 (2014) · 25 pages, 3 figures, 4 tables, CMB, lensing
arxiv created 2014/01/22 · openalex publication_date 2014/06/20 · arxiv updated 2014/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Planck mission has conclusively detected lensing of the cosmic microwave background (CMB) radiation from foreground sources to an overall significance of greater than 25\ensuremathσ [1]. The high precision of this measurement motivates the development of a more complete formulation of the calculation of this effect. While most effects on the CMB anisotropies are widely studied through direct solutions of the Boltzmann equation, the nonlinear effect of CMB lensing is formulated through the solutions of the geodesic equation. In this paper, we present a new formalism to the calculation of the lensing effect by directly solving the Boltzmann equation, as we did in the calculation of the CMB anisotropies at recombination. In particular, we developed a diagrammatic approach to efficiently keep track of all the interaction terms and calculate all possible nontrivial correlations to arbitrary high orders. Using this formalism, we explicitly articulate the approximations required to recover the usual remapping approach used in current studies of the weak lensing. In addition, we point out additional unexplored corrections that are manifest in our formalism to which experiments may be sensitive. As an example, we calculate the correction to the CMB temperature power spectrum for the lens-lens coupling effects which are neglected in standard calculations. We find that the correction is \ensuremath\lesssim0.1% of the CMB temperature power spectrum for \ensuremathℓ up to 3000 and thus is comparable to the cosmic variance.