CAMB: Dark Energy Perturbations
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CAMB: Dark Energy Perturbations
I posted this on an old thread, so maybe no one saw it...
Setting w=-0.9, Omega_DE=0.73, Omega_K=0, I run CAMB to get transfer functions with and without dark energy perturbations. I find that adding the perturbations increases T(k) on large scales and decreases it on small scales. I don't understand why the latter should be true unless there is some subtle normalization going on. I am not using COBE normalization - I am inputting the same scalar amplitude (2.57E-9 at k=.05) each time.
Can anyone explain this?
As a consequence, when I take derivatives with respect to w, the derivatives on small scales depends on whether DE perturbations are on or not.
Thanks,
Chaz
Setting w=-0.9, Omega_DE=0.73, Omega_K=0, I run CAMB to get transfer functions with and without dark energy perturbations. I find that adding the perturbations increases T(k) on large scales and decreases it on small scales. I don't understand why the latter should be true unless there is some subtle normalization going on. I am not using COBE normalization - I am inputting the same scalar amplitude (2.57E-9 at k=.05) each time.
Can anyone explain this?
As a consequence, when I take derivatives with respect to w, the derivatives on small scales depends on whether DE perturbations are on or not.
Thanks,
Chaz
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Re: CAMB: Dark Energy Perturbations
I actually thought that this was right: dark energy anti-clusters with the matter, so slightly suppresses the power. cf
gr-qc/0612027
astro-ph/0203507
http://cosmologist.info/notes/DarkEnergy.ps.gz
The transfer functions agree if you calculate them at redshift 2, so it is just a late-time dark energy effect.
gr-qc/0612027
astro-ph/0203507
http://cosmologist.info/notes/DarkEnergy.ps.gz
The transfer functions agree if you calculate them at redshift 2, so it is just a late-time dark energy effect.
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Re: CAMB: Dark Energy Perturbations
Actually I'm not sure this is right on small scales. The dark energy perturbation is very small compared to the CDM one on small scales, and
[tex]
\Delta_c'' + \mathcal{H} \Delta_c' = 4\pi G a^2 \rho_m \Delta_c
[/tex]
to good accuracy (i.e. the dark energy perturbation contribution to the RHS is negligible). The solution to the above is consistent with CAMB's calculation of \Delta_c with perturbations turned on.
With perturbations turned off the situation is murkier because the equations are then inconsistent (c.f. http://cosmocoffee.info/viewtopic.php?t=512). In fact the numerical solution may depend on how exactly (inconsistently) you force the perturbations to zero, so different codes could give different answers even if both in the synchronous gauge. I guess the main thing is to check that the perturbed result is correct.
[tex]
\Delta_c'' + \mathcal{H} \Delta_c' = 4\pi G a^2 \rho_m \Delta_c
[/tex]
to good accuracy (i.e. the dark energy perturbation contribution to the RHS is negligible). The solution to the above is consistent with CAMB's calculation of \Delta_c with perturbations turned on.
With perturbations turned off the situation is murkier because the equations are then inconsistent (c.f. http://cosmocoffee.info/viewtopic.php?t=512). In fact the numerical solution may depend on how exactly (inconsistently) you force the perturbations to zero, so different codes could give different answers even if both in the synchronous gauge. I guess the main thing is to check that the perturbed result is correct.
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CAMB: Dark Energy Perturbations
I understand that it's difficult to know the correct answer with dark energy perturbations switched off because perfectly smooth dark energy is inconsistent. But I'm still confused on this purely practical point: if the dark energy contribution to the right hand side of the equation is negligible on small scales, why does removing it induce percent-level corrections to the matter power spectrum?
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Re: CAMB: Dark Energy Perturbations
It doesn't if you remove it from that equation, but CAMB isn't using that equation. The effect seems to come via the velocity (which in synchronous gauge are larger than the density perturbation for de) which enters into the evolution equation of \eta; \eta is then used to calculate h' which sources the CDM perturbations. The two methods are only equivalent if the equations are consistent.
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CAMB: Dark Energy Perturbations
I see. Well... my original interest in turning off dark energy perturbations was just so that I could vary DETF parameters (w_0, w_a) without worry (I don't much care about large scales). But it looks like you ultimately advise against running CAMB with no dark energy perturbations. Can the quintessence module mentioned on camb.info be easily adapted in terms of (w_0, w_a) ?
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Re: CAMB: Dark Energy Perturbations
It's easier to modify the default code for w_0 and w_a constant. You just need to add one w' term to the evolution equation (see the CAMB notes) and modify the background.
The other quintessence equations file I have takes a function that returns a potential.
The other quintessence equations file I have takes a function that returns a potential.
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CAMB: Dark Energy Perturbations
Isn't it possible to get no perturbations by having c_s taken to infinity? (As far as I can tell, given Anthony's warnings here, the code does not do that and rather just refuses to compute the DE perturbations in the gauge it works in.)
Or does that acausality somehow wreck the equations and require ad-hoc decisions similar to choosing a gauge?
Or does that acausality somehow wreck the equations and require ad-hoc decisions similar to choosing a gauge?
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CAMB: Dark Energy Perturbations
Simon,
Funny that you should mention this now. We have just posted a paper to arXiv (to appear tomorrow evening) which considers cosmology with [tex]c_s=\infty[/tex] (what we call Cuscuton cosmology). The answer to your question is, no, everything is well-behaved in this limit and perturbations don't go to zero.
We also had an earlier paper which studied causality with [tex]c_s=\infty[/tex] (hep-th/0609150), where we concluded that the theory is causal, as the field equation reduces to a cosntraint equation.
I think this is a really interesting field theory with unique features that I have not seen anywhere else is physics.
Funny that you should mention this now. We have just posted a paper to arXiv (to appear tomorrow evening) which considers cosmology with [tex]c_s=\infty[/tex] (what we call Cuscuton cosmology). The answer to your question is, no, everything is well-behaved in this limit and perturbations don't go to zero.
We also had an earlier paper which studied causality with [tex]c_s=\infty[/tex] (hep-th/0609150), where we concluded that the theory is causal, as the field equation reduces to a cosntraint equation.
I think this is a really interesting field theory with unique features that I have not seen anywhere else is physics.
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CAMB: Dark Energy Perturbations
Hey Niayesh -- oh yes, I remember your cuscheton cosmology from the talk Ghazal (I think) gave at Perimeter. One thing I didn't take away from that -- but know now -- is that the method of construction is literally taking c_s to infinity (I thought you began with a Lagrangian and worked forwards...)
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CAMB: Dark Energy Perturbations
Simon,
There is nothing weird heppening at [tex]c_s=\infty[/tex], i.e. the limit is very well-defined. You can see this in the Fig. 4 of astro-ph/0702002 (which just appeard online). For example, the CMB spectrum at l=2, only changes by 5% from c_s=1 to c_s=10. While our analytic calculations uses [tex]c_s=\infty[/tex], our numerical work uses c_s=10 in CMBeasy.
Antony,
I think the option of no DE perturbations should be removed from CAMB. Of course there is no consistenet way of doing it, while it only leads to confusion in the literature (including the WMAP3 paper).
There is nothing weird heppening at [tex]c_s=\infty[/tex], i.e. the limit is very well-defined. You can see this in the Fig. 4 of astro-ph/0702002 (which just appeard online). For example, the CMB spectrum at l=2, only changes by 5% from c_s=1 to c_s=10. While our analytic calculations uses [tex]c_s=\infty[/tex], our numerical work uses c_s=10 in CMBeasy.
Antony,
I think the option of no DE perturbations should be removed from CAMB. Of course there is no consistenet way of doing it, while it only leads to confusion in the literature (including the WMAP3 paper).
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CAMB: Dark Energy Perturbations
I remember the k-essence model has "strange" c_s behavior, and I think later some folks worked rather hard to check if it implied FTL communication. Then, later, along came some folks, Ruth Durrer I think was one of them, who said it did violate causality. (I dropped some of the first group of folks a line and asked them about it, but didn't hear back.)
I guess what I'm saying is that I don't have a problem with c_s>1 in general, but people do!
I guess what I'm saying is that I don't have a problem with c_s>1 in general, but people do!
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CAMB: Dark Energy Perturbations
"I think the option of no DE perturbations should be removed from CAMB. Of course there is no consistenet way of doing it, while it only leads to confusion in the literature (including the WMAP3 paper)."
I think it should be there still, just so we can check against earlier papers, but highly depricated and perhaps accessible only by setting switches in the code itself. (i.e., I agree with Niayesh as to the issues that seem to be arising.)
I think it should be there still, just so we can check against earlier papers, but highly depricated and perhaps accessible only by setting switches in the code itself. (i.e., I agree with Niayesh as to the issues that seem to be arising.)
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Re: CAMB: Dark Energy Perturbations
This is already the case - it's not an option in the .ini file, you have to hack the code to turn purturbations off. I'll add some references to the cosmocoffee posts to put people off changing it!
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CAMB: Dark Energy Perturbations
Why put people off about changing it or keep it highly depricated ? On the contrary, I believe this option should be accessible through the parameter file from the beginning (besides, the modifications are straight-forward).
This is the point of having a parameter file, isn't it?
This is the point of having a parameter file, isn't it?