Comparing Minimal and Non-Minimal Quintessence Models to 2025 DESI Data

TL;DR

This study tests a broad class of dynamical dark energy scenarios against DESI 2025 data, focusing on canonical quintessence with diverse potentials and on non-minimally coupled scalar fields. Using the CPL-like framework $w_{\rm DE}(a)=w_{0}+(1-a)w_{a}$ and dynamical equations in a flat FLRW background, the authors find that many quintessence potentials yield only modest improvements over $\Lambda$CDM and that none robustly traverses the DESI contours when penalizing extra parameters. Allowing non-minimal coupling to gravity can improve fits in a narrowly tuned region, but introduces a potentially observable fifth force and a time-varying effective gravitational constant $G_{\rm eff}$, which are subject to stringent solar-system and cosmological constraints. Overall, gravity-test constraints tightly limit viable dynamical dark energy models, underscoring the need for broader frameworks or additional ingredients to reconcile DESI hints with a consistent cosmology.

Abstract

In this work we examine the 2025 DESI analysis of dark energy, which suggests that dark energy is evolving in time with an increasing equation of state $w$. We explore a wide range of quintessence models, described by a potential function $V(\varphi)$, including: quadratic potentials, quartic hilltops, double wells, cosine functions, Gaussians, inverse powers. We find that while some provide improvement in fitting to the data, compared to a cosmological constant, the improvement is only modest. We then consider non-minimally coupled scalars which can help fit the data by providing an effective equation of state that temporarily obeys $w<-1$ and then relaxes to $w>-1$. Since the scalar is very light, this leads to a fifth force and to time evolution in the effective gravitational strength, which are both tightly constrained by tests of gravity. For a very narrow range of carefully selected non-minimal couplings we are able to evade these bounds, but not for generic values.

Figures (9)

• Figure 1: Potentials $V(\varphi)$ considered in this work. Left: Blue is quadratic hilltop eq. (\ref{['V1']}), red is quartic hilltop eq. (\ref{['V2']}), green is double well with $\lambda=1$ eq. (\ref{['V3']}), orange is cosine eq. (\ref{['V4']}). Right: Blue is linear monomial eq. (\ref{['V10']}), red is quadratic monomial eq. (\ref{['V5']}), green is quartic monomial eq. (\ref{['V6']}), orange is Gaussian eq. (\ref{['V7']}), purple is inverse function eq. (\ref{['V8']}), pink is inverse square root function eq. (\ref{['V9']}). We have set $k=1$ throughout.
• Figure 2: Top left: Value of the scalar field as a function of time. Top right: Fractional energy densities of matter (red) and dark energy (blue). The vertical dashed line (orange) corresponds to the current time, defined as the moment at which the dark energy density fraction becomes $\Omega_{DE,0}=0.69$, which in this case is $t_0\approx 1.58 m^{-1}$. Bottom: Dark energy equation of state $w$ as a function of the scale factor (solid curve) and CPL fit (blue dashed line). The vertical lines indicate the range over which DESI is most sensitive. The present time is at $a=1$. These plots are for the linear potential eq. (\ref{['V10']}) with $\varphi_i=M_p$.
• Figure 3: Equation of state parameters $w_a$ versus $w_0$. Top left is quadratic hilltop potential eq. (\ref{['V1']}). Top right is quartic hilltop potential eq. (\ref{['V2']}). Bottom left is double well potential with $\lambda=1$ eq. (\ref{['V3']}). Bottom right is cosine potential eq. (\ref{['V4']}). Red is $k = 1$, pink is $k = 2$, purple is $k = 3$, brown is $k = 4$, and black is $k = 5$. We are varying $\varphi_i$ up to its maximum value. Also, the three different contours correspond approximately to the 95% region of the datasets DESI BAO + CMB + PantheonPlus (blue), DESI BAO + CMB + Union3 (orange), DESI BAO + CMB + DESY5 (green), and DESI BAO + CMB (magenta) from Ref. DESI:2025zgx.
• Figure 4: Equation of state parameters $w_a$ versus $w_0$. Top is pure linear potential eq. (\ref{['V10']}). Left is pure quadratic potential eq. (\ref{['V5']}). Right is pure quartic potential eq. (\ref{['V6']}). We are varying $\varphi_i$ from its minimum value. Also, the three different contours correspond approximately to the 95% region of the datasets DESI BAO + CMB + PantheonPlus (blue), DESI BAO + CMB + Union3 (orange), DESI BAO + CMB + DESY5 (green), and DESI BAO + CMB (magenta) from Ref. DESI:2025zgx.
• Figure 5: Equation of state parameters $w_a$ versus $w_0$. Top is Gaussian potential eq. (\ref{['V7']}). Bottom left is inverse potential eq. (\ref{['V8']}). Bottom right is inverse square root potential eq. (\ref{['V9']}). Red is $k = 1$, pink is $k = 2$, purple is $k = 3$, brown is $k = 4$, and black is $k = 5$. We are varying $\varphi_i$ to large values. The inverse potentials continue to loop around to the cosmological constant point. Also, the three different contours correspond approximately to the 95% region of the datasets DESI BAO + CMB + PantheonPlus (blue), DESI BAO + CMB + Union3 (orange), DESI BAO + CMB + DESY5 (green), and DESI BAO + CMB (magenta) from Ref. DESI:2025zgx.