Fisher matrix for the one-loop galaxy power spectrum: measuring expansion and growth rates without assuming a cosmological model

Understand

We introduce a methodology to extend the Fisher matrix forecasts to mildly non-linear scales without the need of selecting a cosmological model.

• We make use of standard non-linear perturbation theory for biased tracers complemented by counterterms, and assume that the cosmological distances can be measured accurately with standard candles.
• Instead of choosing a specific model, we parametrize the linear power spectrum and the growth rate in several $k$ and $z$ bins.
• We show that one can then obtain model-independent constraints of the expansion rate $E(z)=H(z)/H_0$ and the growth rate $f(k,z)$, besides the bias functions.