Fisher matrix for the one-loop galaxy power spectrum

• Verfasst von: Amendola, Luca [VerfasserIn]
• Verfasst von: Pietroni, Massimo [VerfasserIn]
• Verfasst von: Quartin, Miguel [VerfasserIn]
• Titel: Fisher matrix for the one-loop galaxy power spectrum
• Titelzusatz: measuring expansion and growth rates without assuming a cosmological model
• Verf.angabe: Luca Amendola, Massimo Pietroni, and Miguel Quartin
• Ausgabe: Version v2
• E-Jahr: 2022
• Jahr: 17 Sept 2022
• Umfang: 26 S.
• Fussnoten: Version 1 vom 1. Mai 2022, 2. Version vom 17. September 2022 ; Gesehen am 26.10.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2022
• Band/Heft Quelle: (2022), Artikel-ID 2205.00569, Seite 1-26
• DOI: doi:10.48550/arXiv.2205.00569
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Astrophysics - Cosmology and Nongalactic Astrophysics
• Sach-SW: High Energy Physics - Phenomenology
• K10plus-PPN: 1804109223

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 $H(z)/H_0$ 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.