Necessity of ns and sigma8 when providing an input matter power spectrum

[dljarque]

I noticed that CoLoRe requires the cosmological parameters ns and sigma8 in the configuration file even when a linear matter power spectrum P(k) is provided as input.

My understanding is that the spectral index ns should already be encoded in the shape of the input P(k), and similarly the overall normalization (e.g. sigma8 or equivalently As) should already be encoded in its amplitude.

Looking through the code, it seems that sigma8 is used to rescale the primordial amplitude As, but if the input matter power spectrum is already supplied, I would expect this normalization information to be contained in the input spectrum itself.

Could someone clarify why ns and sigma8 are still required in this case? Are they used elsewhere in the calculation, or are they effectively ignored when an external linear matter power spectrum is provided?

[damonge]

Hi @dljarque . n_s is used to extrapolate the P_k at low k if necessary. We rescale the input power spectrum to the desired value of sigma8. If you prefer to avoid both of these operations, you only need to provide the power spectrum down to sufficiently low k (which is usually the case anyway), and to ensure you pass its true sigma8 value. We could have a switch that avoids the sigma8 rescaling altogether. This hadn't become a problem for anyone yet, but it is easy to implement if useful.

[andreufont]

Thanks David for explaining the need for these two parameters, it makes sense now.

No need to change anything in the code, if anything we could add a line or two in the documentation of the config file.