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 [Formula: see text]CDM ([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 text]CDM model more than the [Formula: see text]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 [Formula: see text]CDM 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 text]CDM 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 text]CDM model is favored for [Formula: see text] and [Formula: see text]. Meanwhile, the [Formula: see text]CDM 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.