cosmicjellyfish.LSSsurvey.gcsp_intermediate#

Intermediate-parameter forecast for spectroscopic galaxy clustering.

The Euclid forecast-validation paper (Euclid preparation VII, section 4.2.1) splits the galaxy-clustering Fisher analysis into two stages. First it differentiates the observed power spectrum with respect to an intermediate parameter set made of

  • four shape parameters \(\omega_{b,0}, h, \omega_{m,0}, n_s\),

  • two background parameters per redshift bin, \(\ln D_A(z_i)\) and \(\ln H(z_i)\),

  • two growth parameters per bin, \(\ln f\sigma_8(z_i)\) and \(\ln b\sigma_8(z_i)\),

  • one shot-noise amplitude per bin, \(P_s(z_i)\),

and then projects the resulting Fisher matrix onto the final cosmological parameters with the Jacobian of the intermediate-to-final map.

This module implements that recipe on top of the validated JaxSpectroObservable. The observable is written in the \(f\sigma_8\)/ \(b\sigma_8\) form and is algebraically identical to the validated bfs8terms=False observable at the fiducial point. Both paper-style finite differences and JAX automatic differentiation are available on the same function, so the two derivative engines can be compared directly.

The projection is the Fisher-space chain rule,

\[F_{\alpha\beta} = J^{T}_{\alpha i} F_{ij} J_{j\beta}, \qquad J_{i\beta} = \frac{\partial \theta_i^{\rm int}}{\partial \theta_\beta^{\rm final}},\]

where the intermediate Fisher matrix has already been marginalised over the observational nuisances \(b\sigma_8(z_i)\) and \(P_s(z_i)\). This is not the covariance pull-back \(A^{T} F^{-1} A\) implemented by fisher_derived.

Classes

GCspIntermediateForecast

End-to-end intermediate-parameter Fisher forecast for GCsp.

IntermediateSpectroObservable

Spectroscopic galaxy-clustering observable in intermediate parameters.