A Dynamical Scalar Field Model for Dark Energy: Addressing the Hubble Tension and Cosmic Evolution

TL;DR

This work proposes a dynamical dark energy model based on a canonical scalar field with a hybrid potential $V(\phi)=V_{0}e^{-\lambda\phi}+V_{1}\phi^{n}$ to address the $H_0$ tension and cosmic evolution. Implemented in hi_CLASS and explored with MontePython, the model constrains an 11-parameter space using Planck 2018, BAO, Pantheon+, SH0ES, CC $H(z)$, and SDSS $P(k)$ data, achieving $\chi^2_{red}=0.989$ and $H_0=72.820^{+1.585}_{-0.993}$ km s$^{-1}$ Mpc$^{-1}$, with a thawing regime $\lambda=0.056^{+0.019}_{-0.016}$ giving $w(z=0)\approx-0.85$. While the Bayesian Information Criterion slightly favors $\Lambda$CDM ($\Delta\text{BIC}=+2.178$) due to extra parameters, the model delivers a compelling late-time behavior that reconciles local and early-universe measurements without perturbing early-universe physics. The results motivate further theoretical work on PNGB-inspired UV completions and future surveys (DESI, Euclid) to map the time evolution of $w(z)$ more precisely.

Abstract

We propose a dynamical dark energy model based on a canonical scalar field with a hybrid potential of the form $V(φ) = V_{0}e^{-λφ} + V_{1}φ^{n}$. We constrain the model's 11-dimensional parameter space using a comprehensive combination of cosmological data, including the Planck 2018 Cosmic Microwave Background (CMB) power spectra, Baryon Acoustic Oscillations (BAO), the Pantheon+ supernova sample, SH0ES and the matter power spectrum from SDSS. The model provides an excellent fit to the data, with a reduced chi-squared of $χ^2_{\text{red}} = 0.989$, while successfully alleviating the Hubble constant tension. Our analysis yields a Hubble constant of $H_0 \approx 72.820$ km/s/Mpc, reducing the discrepancy between early and late-universe measurements. We find that the data favors a 'thawing' quintessence scenario, characterized by a potential slope parameter $λ\approx 0.056$. This small but non-zero slope drives a late-time deviation from $Λ$CDM ($w(z=0) \approx -0.85$) while preserving the standard expansion history at high redshifts. A model comparison using the Bayesian Information Criterion finds that the standard $Λ$CDM model is still slightly preferred ($Δ\text{BIC} = 2.178$) due to its fewer parameters. Nevertheless, our results demonstrate that this hybrid potential model is a compelling, physically motivated alternative to a cosmological constant.

Figures (6)

• Figure 1: The full corner plot showing the one- and two-dimensional marginalized posterior distributions for the 11 parameters of our hybrid scalar field model, obtained from the MCMC analysis.
• Figure 2: Comparison of the 1D marginalized posterior distributions (blue histograms) with their corresponding uniform prior distributions (red dashed lines). The tight constraint on all parameters, with posteriors significantly narrower than the priors, demonstrates that the results are strongly data-driven.
• Figure 3: The CMB TT angular power spectrum. The red solid line shows the best-fit prediction from our hybrid scalar field model, while the black points with error bars represent the binned observational data from the Planck 2018 legacy release Planck2018_V_Likelihoods. The model provides an excellent fit to the data across all angular scales.
• Figure 4: The matter power spectrum $P(k)$ at $z=0$. The red line shows the prediction from our best-fit model, which is in excellent agreement with the binned observational data from the SDSS DR7 LRG sample (black points) Reid2010.
• Figure 5: Dynamical evolution of the best-fit Scalar Field model (red solid lines) compared to $\Lambda$CDM (black dashed lines).