Fisher matrix for the one-loop galaxy power spectrum: measuring expansion and growth rates without assuming a cosmological model
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 m...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
17 Sept 2022
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| Edition: | Version v2 |
| In: |
Arxiv
Year: 2022, Pages: 1-26 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2205.00569
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| Author Notes: | Luca Amendola, Massimo Pietroni, and Miguel Quartin |
| Summary: | 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 $H(z)/H_0$ and the growth rate $f(k,z)$, besides the bias functions. We apply the technique to both Euclid and DESI public specifications in the redshift range $0.6-1.8$ and show that the precision on $H(z)$ from increasing the cut-off scale improves abruptly for $k_{\rm max} > 0.17\,h$/Mpc and reaches subpercent values for $k_{\rm max} \approx 0.3\,h$/Mpc. Overall, the gain in precision when going from $k_{\rm max} = 0.1\,h$/Mpc to $k_{\rm max} = 0.3\,h$/Mpc is around one order of magnitude. The growth rate has in general much weaker constraints, unless is assumed to be $k$-independent. In such case, the gain is similar to the one for $H(z)$ and one can reach uncertainties around 5--10\% at each $z$-bin. We also discuss how neglecting the non-linear corrections can have a large effect on the constraints even for $k_{\rm max}=0.1\,h/$Mpc, unless one has independent strong prior information on the non-linear parameters. |
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| Item Description: | Version 1 vom 1. Mai 2022, 2. Version vom 17. September 2022 Gesehen am 26.10.2022 |
| Physical Description: | Online Resource |