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

Abstract We introduce a methodology to extend the Fisher matrix forecasts mildly non-linear scales without need of selecting cosmological model. make use standard perturbation theory for biased tracers complemented by counterterms, and assume that distances can be measured accurately with candles. Instead choosing specific model, we parametrize linear power spectrum growth rate in several k z bins. show one then obtain model-independent constraints expansion E ( ) = )/ H 0 f k,z ), besides bias functions. apply technique both Euclid DESI public specifications range 0.6 ≤ 1.8 gain precision when going from max 0.1 0.2 h /Mpc is around two- threefold, while it reaches four- ninefold extending 0.3 /Mpc. In absolute terms, /Mpc, reach high on at each -shell: 8–10% Δ 0.1, 5–6% 0.2–0.3. This improves 1–2% if taken -independent. The itself has general much weaker constraints, unless assumed -independent, which case similar uncertainties 5–15% reached -bin. also discuss how neglecting corrections have large effect even independent strong prior information parameters.