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Sebastian Bocquet
Joined: 21 Feb 2012 Posts: 3 Affiliation: USM Munich

Posted: February 21 2012 


I am currently working on a formalism that yields a growth factor which is a function of redshift only (no kdependence).
This works fine on small scales (high k), where the growth factor indeed is nearly independent of k; however, it fails to match CAMB's predictions on very large scales >Gpc. I guess this is due to the crossing of the Hubble scale which suppresses the growth of structure.
My question is:
Where and how does CAMB account for this effect?
Any good reference as for formulae?
Many thanks! 

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Antony Lewis
Joined: 23 Sep 2004 Posts: 1309 Affiliation: University of Sussex

Posted: February 21 2012 


CAMB evolves the full linear perturbation theory equations.
The synchonousgauge total matter density perturbation should grow in a kindependent way in most models on large scales (though the Newtonian gauge density perturbation will change due to the horizon scale  see eg. 1105.5292). 

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Sebastian Bocquet
Joined: 21 Feb 2012 Posts: 3 Affiliation: USM Munich

Posted: February 23 2012 


Thanks Antony for that quick reply.
I know that CAMB evolves the full equations; I am trying to understand the evolution as a scale independent growth factor.
I plotted powerspectra at different redshifts ("normalised" at low k) and am now wondering about this kdependence.
ps_z_evo.ps
Could you please help me understanding this behaviour?
Many thanks! 

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Antony Lewis
Joined: 23 Sep 2004 Posts: 1309 Affiliation: University of Sussex

Posted: February 24 2012 


As far as I can see this is a physical effect. I think the synchronousgauge total density perturbation only grows in a scaleindependent way to the extent that pressureless matter dominates the perurbation densities, the total density is comoving with the CDM, the contribution of decaying modes is negligible (or at least their contribution is scale independent), and the baryons are uninteracting.
Just at the moment I can't put my finger on a single effect that simply explains what you see, but the effect is significantly smaller on the largestscales if you plot the power spectrum of the total comoving density perturbation rather than the default synchonous (CDMcomoving) one. 

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Sebastian Bocquet
Joined: 21 Feb 2012 Posts: 3 Affiliation: USM Munich

Posted: February 27 2012 


Thanks again!
What is the easiest way then to obtain the power spectrum of the total comoving density perturbation from CAMB? Are both (synchronous and Newtonian) just related by
Δ_{N}^{i}=Δ^{i}  3Hσ/k
so that I only have to sum over CDM and dark energy for low redshifts and add the 3Hσ/k term to my results? 

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Antony Lewis
Joined: 23 Sep 2004 Posts: 1309 Affiliation: University of Sussex

Posted: April 02 2012 


For the record here are some plots of the synchronousgauge totalmatter growth rate at some different large scales:
(the naive matter dominated result would give 0 on the left axis).
I've not checked the analytics, but would guess the physical picture for the main effect is that while adiabatic modes are outside the horizon Δ_{m} = 3Δ_{R} / 4. At relatively high redshift the radiation density contributes significantly, setting up faster infall velocity than if Ω_{R} = 0 (R=radiation). When the mode enters the horizon, Δ_{R} falls to nearly 0 due to freestreaming of the radiation, and the growth rate slows slightly compared to a similar mode still outside the horizon. Larger modes will have higher growth rate, and this velocity difference will persist (redshifting , and hence corresponding to a decaying mode) some time after the mode enters the horizon, giving scaledependent growth rate until the velocity differences have redshifted to being negligible.
Modes that enter the horizon after matter radiation equality correspond to relatively low perturbation amplitudes and small effects can be relatively more important. 

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