late-time acceleration of the universe, the spectrum of anisotropies of the CMB radiation, and the large-scale structure of matter distribution at the linear level are well described by the base cosmology scenario. The newest results of Planck-2015 indicate that there are still some anomalies that are incompatible with the predictions of the base cosmology scenario [@3], specifically, the anomalies of the observed Hubble parameter $H(z)$ and the higher amplitude of the fluctuation spectrum than that inferred from some analyses of rich cluster counts and weak gravitational lensing. Apart from these anomalies, the $\Lambda$CDM scenario also faces the challenge of two fatal problems, i.e., the “fine-tuning” problem and the “coincidence” problem (see Ref. [@4] for details). In addition, Witten proposed that a positive cosmological constant $\Lambda$ is inconsistent with perturbed string theory [@5]. Therefore, the base cosmology scenario may not reflect the behaviors of the true universe. Based on this concern, numerous alternative dark energy scenarios have been proposed by theorists in recent years, for instance, phantom [@6], quintessence [@7; @8; @9; @10; @11; @12; @13; @14], decaying vacuum [@15], dark fluid [@16; @17; @18; @19; @20; @21], and Chaplygin gas [@22]. The second approach is to introduce modifications to the 