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

TL;DR

This paper extends dark energy modeling to a two-component framework (two-component $w_{2}$CDM) to address the Hubble tension. By fixing one component's EOS at $w_{\rm de1}=-1$ and varying the second component's EOS $w_{\rm de2}$ and fraction $f_{\rm de2}$, the authors map $H_0$ and $\chi^2$ using Planck 2018, BAO, and Pantheon data within a CosmoMC/CAMB setup. They find near-linear dependence of $H_0$ on $f_{\rm de2}$ for fixed $w_{\rm de2}$ and derive explicit fitting formulas showing that $w_{\rm de2}<-1$ with larger $f_{\rm de2}$ can raise $H_0$ enough to alleviate the tension, while $\chi^2$ remains largely comparable to $\Lambda$CDM. The quadratic $\chi^2$ mapping provides high-precision predictions but does not yield a clear $\chi^2$ superiority over $\Lambda$CDM; nonetheless, the study offers a practical tool for rapid estimation of cosmological observables in the $w_{2}$CDM framework. The results motivate further exploration with expanded parameter ranges and alternative functional mappings to refine the model’s predictive power.

Abstract

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 $χ^2$ 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 $χ^2$. 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 $χ^2$, it still prefers the $Λ$CDM model, and the $w_{\rm{2}}$CDM model will decrease significantly when it approaches the $Λ$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.

Figures (7)

• Figure 1: The lines connecting the data points ($f_{\rm{de2}}$, ${H}_{0}$) under different values of $w_{\rm{de2}}$ are shown. Simultaneously mark the range of $H_0 = 73.04 \pm 1.04$$\mathrm{km\cdot s^{-1}\cdot Mpc^{-1}}$ from SH0ES Riess:2021jrx and $H_0 = 67.8365_{-0.3393}^{+0.3456}$$\mathrm{km\cdot s^{-1}\cdot Mpc^{-1}}$ from our result.
• Figure 2: The lines connecting the data points ($w_{\rm{de2}}$, $k$) and their corresponding linear fitting for Eq.(11).
• Figure 3: The three-dimensional rainbow plot of ${H}_{0}$ with respect to $w_{\rm{de2}}$ and $f_{\rm{de2}}$. The ranges of $H_0 = 73.04 \pm 1.04$$\mathrm{km\cdot s^{-1}\cdot Mpc^{-1}}$ from SH0ES Riess:2021jrx and $H_0 = 67.8365_{-0.3393}^{+0.3456}$$\mathrm{km\cdot s^{-1}\cdot Mpc^{-1}}$ from our result are also marked for reference.
• Figure 4: The connecting lines of data points ($f_{\rm{de2}}$, $\chi^{2}$) under different $w_{\rm{de2}}$ conditions.
• Figure 5: The connection of data points ($w_{\rm{de2}}$, $a$) and the corresponding quadratic function fitting for Eq.(14).