In the present paper, we investigate the cosmographic problem using the bias-variance trade-off. We find that both the z-redshift and the $y=z/(1+z)$-redshift can present a small bias estimation. It means that the cosmography can describe the supernova data more accurately. Minimizing risk, it suggests that cosmography up to the second order is the best approximation. Forecasting the constraint from future measurements, we find that future supernova and redshift drift can significantly improve the constraint, thus having the potential to solve the cosmographic problem. We also exploit the values of cosmography on the deceleration parameter and equation of state of dark energy $w(z)$. We find that supernova cosmography cannot give stable estimations on them. However, much useful information was obtained, such as that the cosmography favors a complicated dark energy with varying $w(z)$, and the derivative $dw/dz<0$ for low redshift. The cosmography is helpful to model the dark energy.
Redshift-binned constraints on the Hubble constant under $Λ$CDM, CPL, and Padé cosmography
Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University(北京师范大学前沿天文与天体物理研究所);School of Physics and Astronomy, Beijing Normal University(北京师范大学物理与天文学院);Institute for Astrophysics, School of Physics, Zhengzhou University(郑州大学物理学院天体物理研究所)
Reconstructing the slope of a nearly flat quintessence potential from cosmography
Institute of Research and Development, Duy Tan University(发展研究院);Faculty of Natural Sciences, Duy Tan University(自然科学学院);Centre for Space Research, North-West University(空间研究中心);Department of Mathematics and Applied Mathematics, University of Cape Town(数学与应用数学系);South African Astronomical Observatory(南非天文台);Department of Physics and Astronomy, Vanderbilt University(物理与天文学系)
Cosmography via stellar archaeology of low-redshift early-type galaxies from SDSS
Scuola Internazionale Superiore di Studi Avanzati (SISSA)(高等国际研究学校);Institute for Fundamental Physics of the Universe (IFPU)(宇宙基础物理研究所);Universitat Heidelberg(海德堡大学);University of Trento(特伦托大学);IRA-INAF(国家天体物理研究所阿布鲁佐天文台);INFN-Sezione di Trieste(意大利国家核物理研究所的里雅斯特分部)