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The double complex symmetric gravitational theory is extended to the parametric symmetric gravitational theory by introducing a parameter β. Hence parametric Friedmann-Robertson-Walker equations are obtained and some characters of dark energy in corresponding spaces are discussed by taking different values of β. In our method some previous results can be included as the special case of our results. It is worth noting that some characters of dark energy can be more intuitively described in our model. By analysis, we can predict that the fate of universe would be a Big Rip in the future, and also find that the state parameters for the two different constraint conditions μφ are consistent with the present cosmological observations.