Statistical analysis with cosmic-expansion-rate measurements and two-point diagnostics

Xiaogang Zheng,Xuheng Ding,Shuo Cao,Zong-Hong Zhu,Marek Biesiada,Sixuan Zhang

doi:10.1140/epjc/s10052-018-5759-3

Abstract

Direct measurements of Hubble parameters H(z) are very useful for cosmological model parameters inference. Based on them, Sahni, Shafieloo and Starobinski introduced a two-point diagnostic Omh^2(z_i, z_j) as an interesting tool for testing the validity of the Lambda hbox {CDM} model. Applying this test they found a tension between observations and predictions of the Lambda hbox {CDM} model. We use the most comprehensive compilation H(z) data from baryon acoustic oscillations (BAO) and differential ages (DA) of passively evolving galaxies to study cosmological models using the Hubble parameters itself and to distinguish whether Lambda hbox {CDM} model is consistent with the observational data with statistical analysis of the corresponding Omh^2(z_i, z_j) two-point diagnostics. Our results show that presently available H(z) data significantly improve the constraints on cosmological parameters. The corresponding statistical Omh^2(z_i, z_j) two-point diagnostics seems to prefer the quintessence with w>-1 over the Lambda hbox {CDM} model. Better and more accurate prior knowledge of the Hubble constant, will considerably improve the performance of the statistical Omh^2(z_i, z_j) method.

Highlights

Such models are known as wCDM and CPL, respectively
H (z) measurements from the so called cosmic chronometers, i.e. differential ages (DA) of passively evolving galaxies are free from any prior assumption concerning cosmology, only uncertainty being of astrophysical origin
There have been some misunderstanding in this respect since additional measurements of H (z) from baryon acoustic oscillations (BAO) peaks location were used in the literature as well

Summary

Introduction

About the way they are calibrated in order not to fall into circularity problems with respect to the cosmological model assumed during the calibration From this perspective, another very attractive probe – Hubble function at different redshifts H (z) – is becoming accessible. Its advantage as a screening test for the CDM (formal function of the redshift Om(z) should be just a constant) is clear Later on, they developed it further by introducing a two-point diagnostic Omh2(zi , z j ) [18]. The two-point diagnostics has an advantage that if we know Hubble parameters at n different redshifts, we can get n(n − 1)/2 pairs of data This enlargement of statistical sample for inference occurs at the expense of nontrivial statistical properties of observables [21].

Data and method

Constraints based on two-point diagnostics

Results and discussion

Conclusion