## CMB lensing and effect on parameters

Antony Lewis
Posts: 1354
Joined: September 23 2004
Affiliation: University of Sussex
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### CMB lensing and effect on parameters

Would cover

1. Small shift on WMAP2 error bars due to lensed power spectrum
2. Discussion of ns-A-tau-ombh2 degeneracy with lensing (made worse)
3. Test mock Planck data to see if power spectrum analysis is sufficient or whether non-Gaussianities need to be fully modelled
4. Effect of lensing on Planck forecasts

Would include documentation of LensPix simulation code.

Any overlaps with other work/suggestions?

Antony Lewis
Posts: 1354
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### CMB lensing and effect on parameters

I'm not sure when I'm going to get round to writing up the conclusions of this. Here's a summary.

Using the lensed $C_l$ seems to work fine for parameter estimation as long as you compute the theoretical result accurately. In particular the 2nd-order perturbative result (e.g. astro-ph/0001303) is not accurate enough. Here's a comparison with the correct result

Red is the 2nd order result, and biases parameters for Planck. The blue result is that of astro-ph/9505109, which is actually pretty much accurate enough for Planck. The very accurate 'correct' result was generated using the Nov 2004 version of CAMB using a new full-sky generalization of the result in astro-ph/9505109 (work with Anthony Challinor).

Using the accurate $C_l$ calculation, for a typical idealized Planck-like simulation I get parameter constraints for a vanilla model like this:

Here black is analysing the lensed sky with the lensed $C_l$, red is analysing the unlensed sky with the unlensed $C_l$, and blue is the wrong result if you analyse the lensed sky but neglect lensing in the $C_l$ calculation. The lensed results neglects non-gaussianity of the lensed field.

[The simulation input model had $n_s = 0.99$, $A_s = 2.5 \times 10^{-9}$, $\Omega_b h^2 = 0.022$, $\Omega_b h^2 = 0.12$, $\tau=0.15$ and $h=0.72$].