An optimal basis system for cosmology: data analysis and new parameterisation

Abstract

We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimised for a specific cosmological model or for an ensemble of models, even if based on drastically different physical assumptions. The projection coefficients derived from this basis system, the so-called features, provide a common parameterisation for studying and comparing different cosmological models independently of their physical construction. They can be used to directly compare different cosmologies and study their degeneracies in terms of a simple metric separation. This is a very convenient approach, since only very few realisations have to be computed, in contrast to Markov-Chain Monte Carlo methods. Finally, the proposed basis system can be applied to reconstruct the Hubble expansion rate from supernova luminosity distance data with the advantage of being sensitive to possible unexpected features in the data set. We test the method both on mock catalogues and on the SuperNova Legacy Survey data set.

7 pages, 5 figures, 1 table, replaced to match version accepted by A&A

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• Model-independent determination of curvature parameter by using $H(z)$ and $D_A(z)$ data pair from BAO measurement
• Nonparametric reconstruction of the cosmic expansion with local regression smoothing and simulation extrapolation
• Model-Independent Reconstruction of the Expansion History of the Universe from Type Ia Supernovae
• Generalised model-independent characterisation of strong gravitational lenses V: reconstructing the lensing distance ratio by supernovae for a general Friedmann universe
• Cosmological Parameter Estimation from SN Ia data: a Model-Independent Approach
• Reconstruction of cosmological matter perturbations in Modified Gravity
• Smoothing expansion rate data to reconstruct cosmological matter perturbations
• Probing the Expansion history of the Universe by Model-Independent Reconstruction from Supernovae and Gamma-Ray Bursts Measurements
• On the sensitivity of weak gravitational lensing to the cosmic expansion function