CAMB: Adiabatic and Isocurvature

[Davide Maino]

Is it possible to specify, AT THE SAME TIME, both adiabatic and isocurvature perturbations? Is there a way to express any possible cross-correlation between them? Is it possible to have a cross-correlation term which is actually a transfer function?

[Antony Lewis]

You can use the initial_vector in the .ini file to set any combination of totally correlated modes (with the same power spectra). If you want partially correlated ones you'd need to run the code multiple times with different settings and combine the results to solve for the combination you want.

[Davide Maino]

Hi Anthony, thanks. Other question: if I run a combination of adiabatic and isocurvature including adiabatic tensor modes, how the tensor-to-scalar ratio is computed? Does it include the scalar isocurvature perturbations? i.e.

[tex] r = \frac{P_R^T}{P_R^S + P_{iso}^S}[/tex]

[Davide Maino]

Hi, is it possible with CAMB to obtain only the correlated part iso/adiab for a given fraction of iso perturbation? I.e. I would like to have

[tex]C_\ell^{tot} = (1-\alpha)C_\ell^{ad} + \alpha|\gamma|C_\ell^{iso}+
{\rm sign}(|\gamma|)\sqrt{\alpha(1-\alpha)|\gamma|}C_\ell^{corr}[/tex]

with a given [tex]\alpha[/tex] and [tex]\gamma[/tex].

[Davide Maino]

How can I have totally anti-correlated mixture of adiabatic and isocurvature modes?

[Antony Lewis]

How can I have totally anti-correlated mixture of adiabatic and isocurvature modes?

Just set the component in initial_vector to be negative (relative to the adiabatic sign, depending on your sign convention).

For the general mixture (with same power spectra) you'd need to run CAMB multiple times with combinations of pure or purely correlated modes, and combine to make what you want.

I think r is defined via the scalar amplitude (same for each component, so equivalent to purely adiabtic ratio if using adiabatic with vector component -1). If in doubt check the source code.