English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Planck mission has conclusively detected lensing of the Cosmic MicrowaveBackground (CMB) radiation from foreground sources to an overall significanceof greater than $25\sigma$. The high precision of this measurement motivatesthe development of a more complete formulation of the calculation of thiseffect. While most effects on the CMB anisotropies are widely studied throughdirect solutions of the Boltzmann equation, the non-linear effect of CMBlensing is formulated through the solutions of the geodesic equation. In thispaper, we present a new formalism to the calculation of the lensing effect by\emph{directly solving the Boltzmann equation}, as we did in the calculation ofthe CMB anisotropies at recombination. In particular, we developed adiagrammatic approach to efficiently keep track of all the interaction termsand calculate all possible non-trivial correlations to arbitrary high orders.Using this formalism, we explicitly articulate the approximations required torecover the usual remapping approach used in current studies of the weaklensing. In addition, we point out additional unexplored corrections that aremanifest in our formalism to which experiments may be sensitive. As an example,we calculate the correction to the CMB temperature power spectrum for the\emph{lens-lens} coupling effects which are neglected in standard calculations.We find that the correction is $\lesssim 0.1\%$ of the CMB temperature powerspectrum for $\ell$ up to 3000 and thus is comparable to the cosmic variance.

Formulating Weak Lensing from the Boltzmann Equation and Application to Lens-lens Couplings