Testing consistency of general relativity with kinematic and dynamical probes

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In this work, we test consistency relations between a kinematic probe, the observational Hubble data, and a dynamical probe, the growth rates for cosmic large scale structure, which should hold if general relativity is the correct theory of gravity on cosmological scales.

• Moreover, we summarize the development history of parametrization in testings and make an improvement of it.
• Taking advantage of the Hubble parameter given from both parametric and non-parametric methods, we propose three equations and test two of them performed by means of two-dimensional parameterizations, including one using trigonometric functions we propose.
• As a result, it is found that the consistency relations satisfies well at $1\sigma$ CL and trigonometric functions turn out to be efficient tools in parameterizations.