Hello,
I take as reference the following link : viewtopic.php?t=475
I would like to understand why one has to to a correction on [math] between the linear and nonlinear regime of CAMB.
Actually, in my code, I launch a first time CAMB in linear regime in order to produce 100 files of matter power spectrum ( one [math] 's file for each of the 100 redshifts considered).
Then, I compute [math] from these matter power spectrum : I call this [math].
So, I make the following computation to on [math] and so calculate its new value : [math]
[math] and [math] represent the fiducial/reference values (As far I know, [math] and [math]
After, I launch again CAMB but now, in nonlinear regime (with Takabird Halofit model) by using [math].
Finally my question is : why have we got to make this correction on [math] between linear ans nonlinear model launching.
Is this for keeping [math] like a parameter of calibration for linear regime ? But this is not [math] which is constant, like for [math], I mean I can't see which quantity remains constant between the 2 CAMB executions (linear and non linear).
If asomeone could explain me what is the goal of this correction on [math] between the 2 runs of CAMB. This would allow me to grasp better the subtilities of the linear and nonlinear model.
Kind regards.
Explanations on making correction on A_s between linear and nonlinear regime

 Posts: 38
 Joined: May 18 2019
 Affiliation: IRAP
 Contact:

 Posts: 1618
 Joined: September 23 2004
 Affiliation: University of Sussex
 Contact:
Re: Explanations on making correction on A_s between linear and nonlinear regime
$\sigma_8$ should be definition be linear and hence independent of the nonlinear model as long as you are only changing $A_s$ (keeping $H_0$ etc fixed)

 Posts: 38
 Joined: May 18 2019
 Affiliation: IRAP
 Contact:
Re: Explanations on making correction on A_s between linear and nonlinear regime
Thanks for your quick answer. The current issue on all this post is about the nonlinear Takabird Halofit model (option 4 in params.ini).
I have doubts about the current relation I am using, i.e :
[math]
Indeed, it is indicated on this link viewtopic.php?t=475 that :
[math]
and finally, we would have instead :
[math]
Question 1) If this is not a right relation, could you tell me why one must have :
[math]
Question 2) Does it mean that if [math] is higher than [math], then one has to make decrease the next [math] with [math] equation ?
Question 3)
Does it mean into my code : After a first run (linear) by taking [math], I compute, from [math], the [math] value.
After, I rerun CAMB in nonlinear regime, by using the same [math] initial value.
Then, into a loop on different little steps, I make vary with this step the cosmological parameter on which I want to compute the corresponding [math] (in my case, I study [math]).
I rerun a third time CAMB (the first time into the loop), by setting again the input value [math] : I compute from output [math] the value [math] and Now, I make the following computation (see equation [math] above) :
[math]
Finally, always on this loop on the steps making vary [math], I launch CAMB a last time (the second time into the loop) with [math], i.e with the corrected previous value of [math] as input value.
And I store all [math] coming from this last run and associated to the current step of variation on [math] value.
I repeat the two last runs of CAMB for each different step iteration.
Question 4) Does all this procedure seem to be correct (first 2 steps with run linear and nonlinear regime, and correction achieved after the first linear run into loop) ?
I hope having been cleared on this issue since with Takabird HALOFIT nonlinear model, the derivative of [math] as respect of [math] presents, at little scales (see attachment for k=0.1 and k=0.2), a cutoff (a sudden peak) at roughly 1e3, for a chosen redshift . At large scales, it is perfectly stable (a large flatness from 1e6 to 1e1) (see attachment for k = 0.001). I would like to find the origin of this peak for k > 0.1.
If you want further informations or more detailled explanations, feel free to let me know it.
Regards
I have doubts about the current relation I am using, i.e :
[math]
Indeed, it is indicated on this link viewtopic.php?t=475 that :
So, if scalar_amp(1) is proportional to [math], shouldn't we have rather the relation :if you set get_transfer = T, \sigma_8 will be computed for whatever your input scalar_amp(1). Since \sigma_8^2 scales like scalar_amp(1)
[math]
and finally, we would have instead :
[math]
Question 1) If this is not a right relation, could you tell me why one must have :
[math]
Question 2) Does it mean that if [math] is higher than [math], then one has to make decrease the next [math] with [math] equation ?
Question 3)
Does it mean into my code : After a first run (linear) by taking [math], I compute, from [math], the [math] value.
After, I rerun CAMB in nonlinear regime, by using the same [math] initial value.
Then, into a loop on different little steps, I make vary with this step the cosmological parameter on which I want to compute the corresponding [math] (in my case, I study [math]).
I rerun a third time CAMB (the first time into the loop), by setting again the input value [math] : I compute from output [math] the value [math] and Now, I make the following computation (see equation [math] above) :
[math]
Finally, always on this loop on the steps making vary [math], I launch CAMB a last time (the second time into the loop) with [math], i.e with the corrected previous value of [math] as input value.
And I store all [math] coming from this last run and associated to the current step of variation on [math] value.
I repeat the two last runs of CAMB for each different step iteration.
Question 4) Does all this procedure seem to be correct (first 2 steps with run linear and nonlinear regime, and correction achieved after the first linear run into loop) ?
I hope having been cleared on this issue since with Takabird HALOFIT nonlinear model, the derivative of [math] as respect of [math] presents, at little scales (see attachment for k=0.1 and k=0.2), a cutoff (a sudden peak) at roughly 1e3, for a chosen redshift . At large scales, it is perfectly stable (a large flatness from 1e6 to 1e1) (see attachment for k = 0.001). I would like to find the origin of this peak for k > 0.1.
If you want further informations or more detailled explanations, feel free to let me know it.
Regards
 Attachments

 dPk_dOm_0.2.png (9.66 KiB) Viewed 1736 times

 dPk_dOm_0.1.png (8.78 KiB) Viewed 1736 times