Somebody has already mentioned on this blog post the importance of gravitational lensing effect on CMB and the necessity somehow to get rid of its signature in a, hopefully soon, measured B-mode spectum to estimate signal due to inflationary processes.
Lensing effects on the CMB power spectra is modeled as a convolution in the harmonic domain between primordial CMB signal and an integral potential, the lensing potential, which is basically the projection of the gravitational potential in the Universe on our line of sight. Its gradient gives us the amplitude of the deviation CMB photons are subjected to.
Up to date two attempts were made to reconstruct the lensing amplitude from the 3yr-WMAP data estimating the deflection field and then cross correlating it with some objects representative of the density field i.e. objects of the NRAO VLA Sky Survey and SDSS. Time has passed by and now 7 year data maps have improved their sensitivity and so why not trying a direct detection of lensing signal on those data?
Quadratic estimators were proposed to extract such signal from CMB data alone conversely the approach implemented in this recent paper is based on type of estimator derived using an approximated angular trispectrum (since lensing induces non-Gaussianities correlating large and small scale power) and a proper weighting of the observed (WMAP) maps which lead to an estimator with good signal to noise.
Combining W and V WMAP frequency channel maps and after having performed a null test to avoid false detection due to experimental bias, they menaged to extract the lensing potential power spectrum up to l=750 with bins with a width of 150. The first detection of lensing potential from CMB data alone!
Once the lensing potential power spectrum being computed, they try to estimate a "lensing amplitude" A_L parameter, describing the amount of lensing in the universe (a 0 values means no lensing" while a 1 means the expected amount of lensing signal) using with different priors on A_L and and including or not the lensing potential power spectrum in the analysis. I don't want to eliminate all the suspense so check the paper!
The effect of lensing on T power spectrum is small so it woud be much more interesting to see how such kind of estimators would work for the polarized case with respect to the optimal quadratic ones (see here and here). According to the author this work is on the way...
Supplementary material is available here.
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