## Linear Evolution in CAMB

Use of Healpix, camb, CLASS, cosmomc, compilers, etc.
Matthew Lewandowski
Posts: 2
Joined: May 10 2016
Affiliation: Stanford University

### Linear Evolution in CAMB

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

$\left( \frac{D(z_1)}{D(z_2)} \right)^2 \frac{P_{CAMB}^{tot.} (k , z_2)}{P_{CAMB}^{tot.} (k , z_1)}$

should be equal to 1 for all k that are inside the horizon, and as long as $z_1$ and $z_2$ 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
Posts: 1379
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).

Matthew Lewandowski
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