Validating the Fisher approach for stage IV spectroscopic surveys

Abstract

In recent years forecasting activities have become a very important tool for designing and optimising large scale structure surveys. To predict the performance of such surveys, the Fisher matrix formalism is frequently used as a fast and easy way to compute constraints on cosmological parameters. Among them lies the study of the properties of dark energy which is one of the main goals in modern cosmology. As so, a metric for the power of a survey to constrain dark energy is provided by the Figure of merit (FoM). This is defined as the inverse of the surface contour given by the joint variance of the dark energy equation of state parameters $\{w_0,w_a\}$ in the Chevallier-Polarski-Linder parameterisation, which can be evaluated from the covariance matrix of the parameters. This covariance matrix is obtained as the inverse of the Fisher matrix. Inversion of an ill-conditioned matrix can result in large errors on the covariance coefficients if the elements of the Fisher matrix have been estimated with insufficient precision. The conditioning number is a metric providing a mathematical lower limit to the required precision for a reliable inversion, but it is often too stringent in practice for Fisher matrices with size larger than $2\times 2$. In this paper we propose a general numerical method to guarantee a certain precision on the inferred constraints, like the FoM. It consists on randomly vibrating (perturbing) the Fisher matrix elements with Gaussian perturbations of a given amplitude, and then evaluating the maximum amplitude that keeps the FoM within the chosen precision. The steps used in the numerical derivatives and integrals involved in the calculation of the Fisher matrix elements can then be chosen accordingly in order to keep the precision of the Fisher matrix elements below this maximum amplitude...

arXiv comment20 pages, 10 figures, 11 tables

References in corpus (29)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Efficient Computation of CMB anisotropies in closed FRW models
• LSST: from Science Drivers to Reference Design and Anticipated Data Products
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
• Exploring the Expansion History of the Universe
• Accelerating Universes with Scaling Dark Matter
• Baryonic Features in the Matter Transfer Function
• The Baryon Oscillation Spectroscopic Survey of SDSS-III
• Dark Energy Survey Year 1 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
• Cosmology and Fundamental Physics with the Euclid Satellite
• The WiggleZ Dark Energy Survey: mapping the distance-redshift relation with baryon acoustic oscillations
• Power Spectra for Cold Dark Matter and its Variants
• The SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Overview and Early Data
• The 2dF Galaxy Redshift Survey: The power spectrum and the matter content of the universe
• Probing Dark Energy with Baryonic Acoustic Oscillations from Future Large Galaxy Redshift Surveys
• Measuring cosmological parameters with galaxy surveys
• Cosmology with Phase 1 of the Square Kilometre Array; Red Book 2018: Technical specifications and performance forecasts
• Core Cosmology Library: Precision Cosmological Predictions for LSST
• Fast and reliable MCMC for cosmological parameter estimation
• Measuring the galaxy power spectrum with future redshift surveys
• Designing a space-based galaxy redshift survey to probe dark energy
• On the Validity of Cosmological Fisher Matrix Forecasts
• Breaking the spell of Gaussianity: forecasting with higher order Fisher matrices
• Dark Energy Constraints from Baryon Acoustic Oscillations
• Forecasts of non-Gaussian parameter spaces using Box-Cox transformations
• A fast, always positive definite and normalizable approximation of non-Gaussian likelihoods
• Dark sectors of the Universe: A Euclid survey approach
• Optimizing parameter constraints: a new tool for Fisher matrix forecasts

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