[astro-ph/0209489] Analyzing weak lensing of the cosmic micr
Posted: September 24 2004
This seems like a nice paper, however some things are rather confusing:
1. p6, "unit determinant of Lambda". Surely the lensing matrix (in any given realisation) does not have unit determinant? Also the claim that the noise and the CMB power are rarely of the same order seems spurious because most of the information for lensing reconstruction will come from the smallest scales that are not noise dominated (i.e. where the noise and cmb are about the same)
2. Section D. The authors use the first order series expansion in this section. Since it is not at all true that this is a good approximation on most scales this may be a very bad approximation. Also setting H[Theta] to H[Theta_hat] is also extremely bad for l>300.
3. p19, estimator map of lensing potential: How do steps (i) and (ii) accomplish a good approximation to [tex]C^{-1}\hat{\Theta}[/tex]?
More generally, can anyone explain why the first order expansion in the lensing potential actually gives a quadratic estimator that is quite accurate? (given that the expansion itself is rather bad). Seems like the expansion is encapsulating most of the non-Gaussianity even though the Gaussian signal is quite wrong on most scales.
1. p6, "unit determinant of Lambda". Surely the lensing matrix (in any given realisation) does not have unit determinant? Also the claim that the noise and the CMB power are rarely of the same order seems spurious because most of the information for lensing reconstruction will come from the smallest scales that are not noise dominated (i.e. where the noise and cmb are about the same)
2. Section D. The authors use the first order series expansion in this section. Since it is not at all true that this is a good approximation on most scales this may be a very bad approximation. Also setting H[Theta] to H[Theta_hat] is also extremely bad for l>300.
3. p19, estimator map of lensing potential: How do steps (i) and (ii) accomplish a good approximation to [tex]C^{-1}\hat{\Theta}[/tex]?
More generally, can anyone explain why the first order expansion in the lensing potential actually gives a quadratic estimator that is quite accurate? (given that the expansion itself is rather bad). Seems like the expansion is encapsulating most of the non-Gaussianity even though the Gaussian signal is quite wrong on most scales.