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 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. We apply the technique to both Euclid and DESI public specifications in the range $0.6\le z\le 1.8$ and show that the gain in precision when going from $k_{\max }=0.1$ to $0.2h$/Mpc is around two- to threefold, while it reaches four- to ninefold when extending to $k_{\max }=0.3h$/Mpc. In absolute terms, with $k_{\max }=0.2h/$Mpc, one can reach high precision on $E(z)$ at each $z$-shell: 8-10% for DESI with $\Delta z=0.1$, 5-6% for Euclid with $\Delta z=0.2-0.3$. 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 $k_{\max }=0.1h/$Mpc, unless one has independent strong prior information on the non-linear parameters.

v3: new appendix E discussing the AP effect under binning of mu and k; code upgraded to include non-diagonal beta(k) entries; accepted for publication in JCAP v2: corrected bug affecting high-k results; included extra FoG-related nuisance parameters; extended discussion and analysis; new Appendix D; 12 new references

References in corpus (28)

• The EAGLE simulations of galaxy formation: calibration of subgrid physics and model variations
• The DESI Experiment Part I: Science,Targeting, and Survey Design
• Simba: Cosmological Simulations with Black Hole Growth and Feedback
• The trouble with $H_0$
• The Effective Field Theory of Cosmological Large Scale Structures
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Anisotropic galaxy clustering in Fourier-space
• 4MOST: Project overview and information for the First Call for Proposals
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in Fourier-space
• The IR-resummed Effective Field Theory of Large Scale Structures
• Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
• A new analysis of galaxy 2-point functions in the BOSS survey, including full-shape information and post-reconstruction BAO
• Multi-Point Propagators in Cosmological Gravitational Instability
• Large-scale dark matter simulations
• A Closure Theory for Non-linear Evolution of Cosmological Power Spectra
• The miniJPAS survey: a preview of the Universe in 56 colours
• Constraints on the curvature of the Universe and dynamical dark energy from the Full-shape and BAO data
• Cosmological constraints from BOSS with analytic covariance matrices
• On the impact of baryons on the halo mass function, bias, and cluster cosmology
• The Redshift Space Momentum Power Spectrum II: measuring the growth rate from the combined 2MTF and 6dFGSv surveys
• Galaxy bias from forward models: linear and second-order bias of IllustrisTNG galaxies
• A coarse grained perturbation theory for the Large Scale Structure, with cosmology and time independence in the UV
• A Reference Survey for Supernova Cosmology with the Nancy Grace Roman Space Telescope
• PT challenge: Validation of ShapeFit on large-volume, high-resolution mocks
• The 6x2pt method: supernova velocities meet multiple tracers
• The lure of sirens: joint distance and velocity measurements with third generation detectors
• Fisher matrix for multiple tracers: model independent constraints on the redshift distortion parameter
• Unraveling the Universe with DESI
• Testing Large-Scale Structure Measurements Against Fisher Matrix Predictions

Cited by in corpus (6)

• Cosmic chronometers to calibrate the ladders and measure the curvature of the Universe. A model-independent study
• Improving precision and accuracy in cosmology with model-independent spectrum and bispectrum
• A model-independent tripartite test of cosmic distance relations
• Unveiling the Universe with Emerging Cosmological Probes
• Comparing the motion of dark matter and standard model particles on cosmological scales
• A model-independent measurement of the expansion and growth rates from BOSS using the FreePower method