Growth Rate Massive Neutrinos

[David Marsh]

Hello there,

I am trying to calculate the growth rate [tex]f=\frac{d \log \delta}{d \log a} = \frac{\dot{\delta}}{\mathcal{H}\delta}[/tex] for a cosmology with massive neutrinos using CAMB. I would like to ask Anthony for some advice on doing this.

In equations.f90, to get [tex]\dot{\delta}_\nu[/tex] I take the element of y associated to [tex]\delta[/tex] in MassiveNuVars and then take the same element of yprime (in the example below this is y(EV%iq0+off_ix)). However in the approximation in the second part of this loop:

Code: Select all

if (EV%MassiveNuApprox) then    
              off_ix = (nu_i-1)*4
              clxnu=y(EV%iq0+off_ix)
              qnu=y(EV%iq0+off_ix+2)
           else
            off_ix = (nu_i-1)*nqmax*(EV%lmaxnu+1) 
            !Integrate over q
            call Nu_Integrate01(a*nu_masses(nu_i),clxnu,qnu,y(EV%iq0+off_ix),y(EV%iq1+off_ix))
            !clxnu_here  = rhonu*clxnu, qnu_here = qnu*rhonu
            qnu=qnu/rhonu
            clxnu = clxnu/rhonu
           endif

where we integrate over q to get clxnu, I don't know what to do. What approximation is this, and what is the corresponding approximation to take for [tex]\dot{\delta}[/tex]?

Thanks in advance for any help.

[Antony Lewis]

I'd just write out the delta you want as a function of a (for any k of interest), then numerically calculate the required growth rate from the output file. See commented code in CalcScalarSources of cmbmain.f90.

The massive neutrino approximations are described in astro-ph/0203507

[David Marsh]

Thank you.