Toward unbiased estimations of the statefinder parameters

TL;DR

This paper identifies biases in standard cosmography for estimating statefinder parameters and introduces a new hierarchical method that improves accuracy and reduces bias, especially at higher redshifts.

Contribution

The paper proposes a novel hierarchical expansion method for the Hubble function that reduces bias and errors in estimating cosmological parameters compared to standard cosmography.

Findings

Hierarchical method outperforms standard cosmography in accuracy

New approach reduces bias in statefinder estimations

Hybrid methods improve performance at low redshifts

Abstract

With the use of simulated supernova catalogs, we show that the statefinder parameters turn out to be poorly and biased estimated by standard cosmography. To this end, we compute their standard deviations and several bias statistics on cosmologies near the concordance model, demonstrating that these are very large, making standard cosmography unsuitable for future and wider compilations of data. To overcome this issue, we propose a new method that consists in introducing the series of the Hubble function into the luminosity distance, instead of considering the usual direct Taylor expansions of the luminosity distance. Moreover, in order to speed up the numerical computations, we estimate the coefficients of our expansions in a hierarchical manner, in which the order of the expansion depends on the redshift of every single piece of data. In addition, we propose two hybrids methods that incorporates standard cosmography at low redshifts. The methods presented here perform better than the standard approach of cosmography both in the errors and bias of the estimated statefinders. We further propose a one-parameter diagnostic to reject non-viable methods in cosmography.