I have tried to perform the following simple sanity check in CAMB, so as to better understand what is included in the output. Basically, I am comparing the total matter power spectrum (adiabatic mode) outputted by CAMB at two different times with the linear evolution (D^2) from one time to the other. I think that these two things should exactly match, since CAMB is solving the linear equations.
In equations, I think that
[tex]\left( \frac{D(z_1)}{D(z_2)} \right)^2 \frac{P_{CAMB}^{tot.} (k , z_2)}{P_{CAMB}^{tot.} (k , z_1)}[/tex]
should be equal to 1 for all k that are inside the horizon, and as long as [tex]z_1[/tex] and [tex]z_2[/tex] are within matter domination. The [tex]D(z)[/tex] here is the linear growth factor which is a solution for linearized continuity and Euler equations. The result was that there is a 4% difference from [tex]z=100[/tex] to [tex]z=0[/tex], and a 0.5% difference from [tex]z=10[/tex] to [tex]z=0[/tex], in the range [tex]k/h[/tex] from [tex]0.1[/tex] to [tex]100[/tex]
Does anyone know what's going on here?
Linear Evolution in CAMB

 Posts: 2
 Joined: May 10 2016
 Affiliation: Stanford University

 Posts: 1364
 Joined: September 23 2004
 Affiliation: University of Sussex
 Contact:
Re: Linear Evolution in CAMB
At high redshift there are effects from radiation and decaying modes. You may have a massive neutrino contributions (massive neutrinos also affect the background evolution, so may depend on how you defined D(z)). And as k gets large you can start to see linear effects of baryons (pressure of baryons becomes large at k~500).

 Posts: 2
 Joined: May 10 2016
 Affiliation: Stanford University
Linear Evolution in CAMB
Hi Anthony, thank you for your quick reply. I am now pretty sure that the mismatch was indeed due to radiation effects. At z=100, these can have percent level effects, and I think that is what I was seeing. Thanks!
Matt
Matt