## traceless part of stress tensor

Use of Healpix, camb, CLASS, cosmomc, compilers, etc.
Angela Chen
Posts: 18
Joined: January 11 2019
Affiliation: University of Michigan

### traceless part of stress tensor

Hi all,

I have a dumb question that how was the traceless part of stress tensor (pic,pir,pig) defined in derivs code, I didn't find it in the CAMB notes...

Thanks!
Angela

Antony Lewis
Posts: 1503
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### Re: traceless part of stress tensor

Just by direct expansion of the stress-energy tensor (Eq 24) where $\Pi = \sum_i \rho_i\pi_i$. You can read off the relevant equations from the multipole equations for $\ell=2$ (e.g. $I_2=\pi_\gamma$).

Angela Chen
Posts: 18
Joined: January 11 2019
Affiliation: University of Michigan

### Re: traceless part of stress tensor

Thanks! another question, if I do the calculation in not no_nu_multipole for massless neutrino all the time and not using the approximation for large ktau modes, would it give me the right physics, just much slower?

Antony Lewis
Posts: 1503
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### Re: traceless part of stress tensor

I should do, though you may need to also increase l_accuracy_boost.