### [astro-ph/0604416] CMB Anisotropies at Second Order I

Posted:

**April 21 2006**This paper attempts to continue a study of the CMB at second order on all scales. This is a complex and subtle task!

I have one general comment: we know that both CMB lensing and SZ are significantly non-linear effects (i.e. they cannot be accurately modelled at only second order). They can however be studied separately in ways which isolate the relevant physicical processes (and in the case of CMB lensing modelled very accurately). Wouldn't it be better to attempt a second order calculation without these effects (assuming a way can be found to define this consistently), then put them in (at above second order) later?

Also Eq 3.21 looks rather like a lensing effect (and this was said explicitly in a talk I heard). However the sign in the second term looks odd: if the signs in the first and second terms were the same it would basically be a perpendicular gradient which is what is expected for lensing. Furthermore for it to be interpreted as lensing the result should be conformally invariant, which implies only a function of \Psi + \Phi (see e.g. astro-ph/0601594). So is this equation correct, and if so what does it mean?

I have one general comment: we know that both CMB lensing and SZ are significantly non-linear effects (i.e. they cannot be accurately modelled at only second order). They can however be studied separately in ways which isolate the relevant physicical processes (and in the case of CMB lensing modelled very accurately). Wouldn't it be better to attempt a second order calculation without these effects (assuming a way can be found to define this consistently), then put them in (at above second order) later?

Also Eq 3.21 looks rather like a lensing effect (and this was said explicitly in a talk I heard). However the sign in the second term looks odd: if the signs in the first and second terms were the same it would basically be a perpendicular gradient which is what is expected for lensing. Furthermore for it to be interpreted as lensing the result should be conformally invariant, which implies only a function of \Psi + \Phi (see e.g. astro-ph/0601594). So is this equation correct, and if so what does it mean?