CAMB initial conditions and arXIv:astro-ph/9904231

[David Marsh]

I have looked at initial conditions in both the CAMB notes, and the referenced paper. There is a correction to [tex]\delta_\gamma[/tex] in CAMB not present in the paper, which goes as omtau. Is this a higher order correction? If so, why is it necessary, and where is it derived?

I also cannot see the definition of [tex]\pi_r[/tex]. I presume it is some multiple of [tex]\sigma_r[/tex] ([tex]\sigma_\nu[/tex] in the reference), but it isn't obvious. The same is true of [tex]G_3[/tex]. The definitions also seem absent from arXiv:astro-ph/0203507 on a first glance.

Many thanks in advance to all who can offer help.

[Antony Lewis]

The omtau terms allow for the effect of matter, as opposed assuming pure radiation domination.

You can find maple derivations at

http://camb.info/theory.html

Also somewhat more generally in mathematica at http://camb.info/jrs/

[tex]\pi_r[/tex] is the (scalar or tensor part of the) neutrino anisotropic stress; scalar definitions should be consistent with the appendix of arXiv:astro-ph/0203507 I think.

[David Marsh]

Thank you so much! I think the mathematica and maple notebooks will be most helpfull.