Testing consistency of general relativity with kinematic and dynamical
  probes
  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. Furthermore, in
order to confirm the validity of our test, we introduce a model of modified
gravity, DGP model and compare the testing results in the cases of
$\Lambda$CDM, "DGP in GR" and DGP model with mock data. It can be seen that it
is the establishing of consistency relations which dominates the results of the
testing. Overall, the present observational Hubble data and growth rate data
favor convincingly that the general relativity is the correct theory of gravity
on cosmological scales.
