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 Linear Evolution in CAMB
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Matthew Lewandowski

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

 Posted: May 10 2016 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 (D2) 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 $\left( \frac{D(z_1)}{D(z_2)} \right)^2 \frac{P_{CAMB}^{tot.} (k , z_2)}{P_{CAMB}^{tot.} (k , z_1)}$ should be equal to 1 for all k that are inside the horizon, and as long as z1 and z2 are within matter domination. The D(z) 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 z = 100 to z = 0, and a 0.5% difference from z = 10 to z = 0, in the range k / h from 0.1 to 100 Does anyone know what's going on here?
Antony Lewis

Joined: 23 Sep 2004
Posts: 1317
Affiliation: University of Sussex

 Posted: May 10 2016 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).
Matthew Lewandowski

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

 Posted: May 19 2016 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
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