Neutrinos background evolution

[ivan rodriguez-montoya]

Hello everybody,
I am trying to adapt CAMB to some more exotic model of neutrinos. The particles in my model start different from radiation behaviour (p [tex]\neq[/tex] 1/3*[tex]\rho[/tex]).

I guess this information should be replaced in the (modules.f90) subroutine Nu_background(am,rhonu,pnu)

Code: Select all

if &#40;am <= am_minp&#41; then
          rhonu=1._dl + const2*am**2  
          pnu=&#40;2-rhonu&#41;/3._dl
          return
        else if &#40;am >= am_maxp&#41; then
          rhonu = 3/&#40;2*const&#41;*&#40;zeta3*am + &#40;15*zeta5&#41;/2/am&#41;
          pnu = 900._dl/120._dl/const*&#40;zeta5-63._dl/4*Zeta7/am**2&#41;/am
          return
        end if        

        d=log&#40;am/am_min&#41;/dlnam+1._dl
        i=int&#40;d&#41;
        d=d-i
       
!  Cubic spline interpolation.
          rhonu=r1&#40;i&#41;+d*&#40;dr1&#40;i&#41;+d*&#40;3._dl*&#40;r1&#40;i+1&#41;-r1&#40;i&#41;&#41;-2._dl*dr1&#40;i&#41; &
               -dr1&#40;i+1&#41;+d*&#40;dr1&#40;i&#41;+dr1&#40;i+1&#41;+2._dl*&#40;r1&#40;i&#41;-r1&#40;i+1&#41;&#41;&#41;&#41;&#41;
          pnu=p1&#40;i&#41;+d*&#40;dp1&#40;i&#41;+d*&#40;3._dl*&#40;p1&#40;i+1&#41;-p1&#40;i&#41;&#41;-2._dl*dp1&#40;i&#41; &
               -dp1&#40;i+1&#41;+d*&#40;dp1&#40;i&#41;+dp1&#40;i+1&#41;+2._dl*&#40;p1&#40;i&#41;-p1&#40;i+1&#41;&#41;&#41;&#41;&#41;
          rhonu=exp&#40;rhonu&#41;
          pnu=exp&#40;pnu&#41;

+ I understand the first possiblity to be the ultra-relativistic limit, but I want to ask... what is the meaning of the second possiblity?

+ I tried to erase the first two posiblities and go direct to the cubic spline
interpolation but the output is ill. Why is not possible to assume directly the third case (which I understand corresponds to nonrelativistic neutrinos)?

+ I find that the key point is to understand the physical (or any) meaning of the parameters
am_minp=1.1*am_min=1.1*0.01=0.011
am_maxp=0.9*am_max=0.9*600 =540
I read that they are the smallest and greatest values of a*m_nu to integrate the distribution function rather than using series, but this does not completely help. How will this parameters change the outputs? Or what are the rules to evaluate them?

In other words, my goal here, is to set [tex]\rho[/tex] in the background as something which evolves different from purely relativistic particles.

I want to thank your attention and advice.

Ivan R.

[Antony Lewis]

In the non-releativistic limit you can do a series exansion in the velocity (see astro-ph/0203507). The switch values are just determined by numerical tests.

For the spline to work you need to have calculated the splining tables for the relevant values. Series results are likely to be more accurate anyway in some limit.