## camb: k-eta_max scaling with lmax at high l

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Licia Verde
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Joined: January 13 2005
Affiliation: ICE (CSIC-IEEC) Barcelona
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### camb: k-eta_max scaling with lmax at high l

Hi,
two questions:

-while at low l the rule of thumb is that k-eta-max_scalar should be >~twice lmax_scalar, does this scaling holds for lmax>5000 -say-? From what I can see it does not, and it goes in the direction of k-eta-max>2 lmax. Is there a rule of thumb that can be applied in this regime?
(yes I could run convergence tests by gradually increasing k_eta_max, but if somebody has done this already, it'll be very useful....)

-Also, up to what lmax is camb safe and tested? what could "go wrong" if one wanted to go at even higer l's (meaning if one wanted to trust the results above lmax)?

It may sound silly, after all secondary CMB starts dominating at l>~5000 or so. But, in a couple of years there will be CMB data up to l=10000. An accurate modeling of secondary effects will require at least some modeling of the primary....

Thnaks.

Antony Lewis
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### Re: camb: k-eta_max scaling with lmax at high l

The accuracy will depend a bit on what you are calculating (for example the lensed BB is much more sensitive to the maximum k than most other things). I believe it should give reasonable results out to high l, though the accuracy will generally be worse at l>2000 (maybe > percent level; it's not very well tested anyway). At ultra high l you can expect things to screw up, at least without boosting accuracy settings.

For plain unlensed C_l I'd have though the k-eta-max rule of thumb should be OK.

Chris D'Andrea
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Joined: June 07 2005
Affiliation: University of Portsmouth

### camb: k-eta_max scaling with lmax at high l

The graph here is a ratio of two models computed using CAMB, where the only difference in parameters or settings between the two is the value of tau (or Z=exp(-2 tau)). The effect of this physically results in a constant ratio between the two models. I would like to know if there is a way to extend the accuracy of CAMB at very high l (note the x axis is log scale). The settings include no lensing, scalars only, the accuracy_boost and l_accuracy_boost both set to 2, l_sample_boost is 1, and k_eta_max (20200) is exactly twice l_max_scalar (10100). Could this be a manifestation that the rule k_eta_max_scalar ~ 2 lmax_scalar breaks down at very high l?
Thank you.

Antony Lewis
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### Re: camb: k-eta_max scaling with lmax at high l

Probably not - the problem is that the unlensed CMB is absolutely tiny on these scales so I can image all sorts of numerical problems kick in; though if you want to track down the problem I'd be happy to add in any fix you find...

I would guess this specific problem is related to late time evolution, so may be better calculating with tau=0, then multiplying the small scale spectrum by the appropriate damping factor.

However I don't really see why you want to calculate something that is totally unobservable? (*much* smaller than lensing and kinetic-SZ/OV on these scales)

There are also problems calculating the lensing potential power spectrum on very small scales. Accuracy boost helps, but ultimately using the Limber approximation would probably be a much better way to go (there's no support for Limber in CAMB at the moment - it always does full spherical calculation which is inefficient on very small scales where Limber is excellent). Note the very small scale lensed CMB only depends on the small scale lensing potential power spectrum, the unlensed CMB is irrelevant on these scales (see e.g. Sec 4 of astro-ph/0601594).

Michael Doran
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### camb: k-eta_max scaling with lmax at high l

Maybe some sort of accuracy estimate could be given by running CAMB vs both gauges of CMBEASY. They are fairly independent. We could run a "plain" vanilla model with and without re-ionization and see how much the curves deviate. Btw: if CAMB uses a swift re-ionization (as CMBFAST and CMBEASY does), then I could imagine that you'll see some deviation like discussed above: this might at the end be physical, not a numerical artefact. But I'm not sure here, we would have to check (see my speeding-up-the boltzmann-code-paper on the effect of the swift re-ionization that the codes use on the photons).
Anyway. We'll compare CAMB vs the two cmbeasy gauges and take a look at the high l values.