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 Formula: see textCDM (Formula: see text) models and conducted numerical research, finding strong observational support when the value of n is small. Based on our results, both the Formula: see text and Akaike information criterion (AIC) favor the Formula: see textCDM model more than the Formula: see textCDM 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 Formula: see textCDM model. To simplify the model, we fix Formula: see text in one component and set the other component to Formula: see text, varying the proportions of both components in the population. Each Formula: see textCDM model is constrained by the Planck PR4, DESI DR2 and PantheonPlus datasets. Under different Formula: see text, we obtain the one-dimensional distribution of Formula: see text with respect to Formula: see text. Further fitting reveals the evolution of Formula: see text under varying Formula: see text and Formula: see text. We perform the same operation on Formula: see text, also obtaining the variation of Formula: see text with respect to Formula: see text and Formula: see text. To evaluate the error of fitting, we introduce two indicators, Formula: see text and MAPE, to quantify the fitting ability of our models. We find that when Formula: see text is less than -1, Formula: see text increases with the decrease of Formula: see text and the increase of Formula: see text, effectively alleviating Formula: see text tension. In terms of Formula: see text, the Formula: see textCDM model is favored for Formula: see text and Formula: see text. Meanwhile, the Formula: see textCDM model also yields better performance at Formula: see text. The good performance of Formula: see text and MAPE further proves that our model has an outstanding fitting effect and high reliability.
Chen et al. (Fri,) studied this question.