摘要
Many schemes have been proposed to define a model-independent con- straint on cosmological dynamics, such as the nonparametric dark energy equation of state ω（z） or the deceleration parameter q（z）. These methods usually contain deriva- tives with respect to observational data with noise. However, there can be large un- certainties when one estimates values with numerical differentiation, especially when noise is significant. We introduce a global numerical differentiation method, first for- mulated by Reinsch, which is smoothed by cubic spline functions, and apply it to the estimation of the transition redshift zt with a simulated expansion rate E（z） based on observational Hubble parameter data. We also discuss some deficiencies and limita-tions of this method.
Many schemes have been proposed to define a model-independent con- straint on cosmological dynamics, such as the nonparametric dark energy equation of state ω（z） or the deceleration parameter q（z）. These methods usually contain deriva- tives with respect to observational data with noise. However, there can be large un- certainties when one estimates values with numerical differentiation, especially when noise is significant. We introduce a global numerical differentiation method, first for- mulated by Reinsch, which is smoothed by cubic spline functions, and apply it to the estimation of the transition redshift zt with a simulated expansion rate E（z） based on observational Hubble parameter data. We also discuss some deficiencies and limita-tions of this method.
基金
Supported by the National Natural Science Foundation of China
