Implications of the Two-Component Dark Energy Model for Hubble Tension

Dark energy plays a crucial role in the evolution of cosmic expansion. In most studies, dark energy is considered a single dynamic component. In fact, multi-component dark energy models may theoretically explain the accelerated expansion of the universe as well. In our previous research, we constructed the $w_{\rm{n}}$CDM ($n=2, 3, 5$) models and conducted numerical research, finding strong observational support when the value of n is small. Based on our results, both the $\chi^2$ and Akaike information criterion (AIC) favor the $w_{\rm{2}}$CDM model more than the $w_0w_{\rm{a}}$CDM model. However, previous studies were limited to two equal-component dark energy models, failing to consider the component proportions as variables. Therefore, we will further explore the $w_{\rm{2}}$CDM model. To simplify the model, we fix $w = -1$ in one component and set the other component to $w_{\rm{de2}}$, varying the proportions of both components in the population. Under different $w_{\rm{de2}}$, we obtain the one-dimensional distribution of ${H}_{0}$ with respect to $f_{\rm{de2}}$. Further fitting reveals the evolution of ${H}_{0}$ under varying $w_{\rm{de2}}$ and $f_{\rm{de2}}$. We also perform the same operation on $\chi^2$. To evaluate the error of fitting, we introduce two indicators, $\text{R}^{2}_{\text{adj}}$ and MAPE, to quantify the fitting ability of our models. We find that when $w_{\rm{de2}}$ is less than -1, ${H}_{0}$ increases with the decrease of $w_{\rm{de2}}$ and the increase of $f_{\rm{de2}}$, effectively alleviating ${H}_{0}$ tension. For $\chi^2$, it still prefers the $\Lambda$CDM model, and the $w_{\rm{2}}$CDM model will decrease significantly when it approaches the $\Lambda$CDM model. The excellent performance of $\text{R}^{2}_{\text{adj}}$ and MAPE further proves that our model has an outstanding fitting effect and extremely high reliability.