CMB lensing and effect on parameters

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Antony Lewis
Posts: 1352
Joined: September 23 2004
Affiliation: University of Sussex
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CMB lensing and effect on parameters

Post by Antony Lewis » September 23 2004

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: 1352
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

CMB lensing and effect on parameters

Post by Antony Lewis » December 06 2004

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 [tex]C_l[/tex] 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

Image

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 [tex]C_l[/tex] calculation, for a typical idealized Planck-like simulation I get parameter constraints for a vanilla model like this:

Image

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

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

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