Toward unbiased estimations of the statefinder parameters

Understand

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.