Author:
Amendola Luca,Pietroni Massimo,Quartin Miguel
Abstract
Abstract
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) = E(z)/H
0 and the growth rate f(k,z), besides the bias functions. We apply the technique
to both Euclid and DESI public specifications in the range 0.6 ≤ z ≤ 1.8 and show that the
gain in precision when going from k
max = 0.1 to 0.2 h/Mpc is around two- to threefold,
while it reaches four- to ninefold when extending to k
max = 0.3 h/Mpc. In absolute
terms, with k
max = 0.2 h/Mpc, one can reach high precision on E(z) at each z-shell:
8–10% for DESI with Δz = 0.1, 5–6% for Euclid with Δz = 0.2–0.3. This improves to
1–2% if the growth rate f is taken to be k-independent. The growth rate itself has in
general much weaker constraints, unless assumed to be k-independent, in which case the gain is
similar to the one for E(z) and uncertainties around 5–15% can be reached at each z-bin. We
also discuss how neglecting the non-linear corrections can have a large effect on the constraints
even for k
max = 0.1 h/Mpc, unless one has independent strong prior information on the
non-linear parameters.
Subject
Astronomy and Astrophysics
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