Sigma(R) in CAMB and the Halo Mass Function

[David Marsh]

I am trying to use CAMB to calculate the halo mass function. As such, I am taking the subroutine "Transfer_Get_sigma8" and calling it at various different [tex]R[/tex] values.

To access the range of halo masses I am interested in [1e7 ,1e15] [tex]h^{-1} M_\odot[/tex], I am required to use [tex]R[/tex] in the range [0.04,10] Mpc.

My question is: how accurate is Transfer_Get_sigma8 over this range of R? Would anyone recommend doing things differently, i.e. outputting P(k) and integrating it with the window function using some other program.

I spline [tex]\sigma(M)[/tex] and take its derivative numerically to use in [tex]dn/d \log M[/tex]. What I get is slightly lower and shallower at low masses than I expect (comparing a LCDM cosmology from CAMB to Fig. 3 of 1103.2134).

Edit: I have found the solution to this. Clearly one must be careful to compute the power spectrum out to large enough k where the window function peaks. CAMB does not extrapolate P(k) and integrate out to infinity, but only as far as kmax.