\frac{d\Omega_{\rm{de}}(z)}{dz}=-\frac{2\Omega_{\rm{de}}(z)(1-\Omega_{\rm{de}}(z))}{1+z}\left(\frac{1}{2}+\frac{\sqrt{\Omega_{\rm{de}}(z)}}{c}\right).
    \end{aligned}$$ Numerically solving the two differential equations with the initial conditions $E(0)=1$ and $\Omega_{\rm de}(0)=1-\Omega_{\rm m}$ will directly give the evolutions of $E(z)$ and $\Omega_{\rm de}(z)$.

Current mainstream cosmological observations
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**SN data:** We use the largest compilation of type Ia supernovae (SN) data in this work, which is named the Pantheon compilation [@Scolnic:2017caz]. The Pantheon compilation consists of 1048 SN data, which is composed of the subset of 279 SN data from the Pan-STARRS1 Medium Deep Survey in the redshift range of $0.03 < z < 0.65$ and useful distance estimates of SN from SDSS, SNLS, various low-redshift and HST samples in the redshift range of $0.01 < z < 2.3$. According to the observational point of view, using a modified version of the Tripp formula [@Tripp], in the SALT2 spectral model [@Guy], the distance modulus can be expressed as [@Scolnic:2017caz] $$\label{SNu}
{\mu}=m_{\rm{B}}-M+\alpha \times x_{1}-\beta \times c +\Delta_{M}+\Delta_{B},$$ where $m_{\rm{B}}$, $x_{1}$, and $c$ represent the log of the overall flux normalization, the light-curve shape parameter, and the color in the light-curve fit of SN, respectively, $M$ repersents the absolute B-band magnitude with $x_{1} = 0$ and $c = 0$ for a fiducial SN, $\alpha$ and $\beta$ are the 