Large Scale value of $\delta_g/4+2\Phi$
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Hi, I am plotting the value of [tex]\delta_g/4+2\Phi[/tex] from the transfer function output file. If you look at its value at large scales ([tex]k=6.96268e-06[/tex]) it's value come out to be ~[tex]0.9[/tex] rather than the Saachs Wolfe factor of [tex]1/5[/tex] or [tex]1/3[/tex]. So, I wanted wanted to ask where I am going wrong with my understanding.
Firstly make sure you are using Newtonian gauge [tex]\delta g[/tex] not the synchronous gauge one output by default. Secondly there are corrections from neutrino anisotropic stress and recombination not being exactly matter dominated.
There's no direct way to get that, you'd have to construct the corresponding gauge invariant combination of synchronous gauge density and shear (which you could infer from the output synchronous gauge density, Newtonian-gauge CDM velocity and the Hubble parameter, using relations described in the CAMB notes p22).