Non-Minimally Coupled Quintessence in Light of DESI

TL;DR

This work investigates a Palatini gravity model in which a canonical scalar field with an exponential potential is non-minimally coupled to gravity via f(φ)=1+ξ φ^2/m_P^2. By formulating the theory in the Jordan frame and solving a dynamical system, the authors identify a late-time de Sitter attractor for negative ξ, independent of the potential slope λ, and show that this model can fit CMB, DESI BAO, and DESY5 SN data better than ΛCDM, with strong Bayesian evidence (log B≈5.52). The analysis finds dynamical dark energy and a phantom crossing in w_phi_eff at ≳3σ, and demonstrates that Palatini dynamics marginally outperform the metric formulation in data concordance. These results imply that non-minimal couplings in alternative gravity theories can alleviate low- and intermediate-redshift tensions, though they raise theoretical questions about varying G and fifth forces that require further investigation.

Abstract

We analyze a model of quintessence governed by an exponential potential and non-minimally coupled to gravity, in light of recent datasets, including cosmic microwave background, baryon acoustic oscillations, and supernovae distance moduli observations. Mainly focusing on the Palatini formulation of gravity, a phase space analysis reveals the existence of a late-time stable de Sitter attractor as long as the non-minimal coupling constant is negative, regardless of the value of the slope of the exponential. Fitting to CMB+DESI+DESY5 data, we find strong evidence for our model over $Λ$CDM, with a Bayes factor $\log B = 5.52$. Furthermore, the data seem to prefer dynamical dark energy at $>3σ$ C.L. and a phantom crossing in the barotropic parameter of dark energy at $2-3σ$ C.L.. We find that the scalar field dynamics in the Palatini formalism provides marginally better agreement to the data compared to the metric formalism.

Figures (10)

• Figure 1: Time evolution of the density parameters of matter (blue), radiation (orange), and quintessence (green), as well as of the effective barotropic parameter of quintessence (red) and the Universe (purple), as a function of the elapsing number of e-folds $N$ and redshift $z$, for the CMB+DESI+DESY5 best-fit parameters $\xi=-1.41$, $\lambda = 1.95$, $\Omega_{\rm m}=0.3193$, $H_0=66.70$km$/$s$/$Mpc, and $\Omega_{\rm b}=0.05049$.
• Figure 2: Phase space slice in the $(x_1,x_2)$ plane for the Palatini (left) and metric (right) formalisms, given the CMB+DESI+DESY5 best-fit parameters $\xi=-1.41$, $\lambda = 1.95$, $\Omega_{\rm m}=0.3193$, $H_0=66.70$km$/$s$/$Mpc, and $\Omega_{\rm b}=0.05049$. The variables $x_3$ and $x_4$ are fixed to their DE-a (red point) attractor values. Both formalisms share the same fixed points but the overall dynamics differ.
• Figure 3: Upper Left: 100 realizations of the effective barotropic parameter of non-minimally coupled quintessence with an exponential potential for the entire integration range $N=[-15,0]$. The values of $\xi$ and $\lambda$ are randomly drawn from the joint 95% credible region in $(\xi,\lambda)$. The rest of the model parameters are fixed to $x_2(-15)=3.00\times 10^{-11}$, $H_0=66.70$ and $\Omega_{\rm b}=0.05050$. Upper Right: Zoomed-in version of the upper left panel focusing on $N=[-3,0]$. Bottom left: 100 realizations of the effective density parameter for the same parameter values as the upper panels, for the entire integration range $N=[-15,0]$. Bottom right: Zoomed-in version of the lower left panel focusing on $N=[-3,0]$.
• Figure 4: BAO distances $D_M(z)/z_d$ (left) $D_H(z)/z_d$ (center) and $D_V(z)/z_d$ (right) predicted by $\xi\phi$CDM (full blue) and $\phi$CDM (dashed orange) relative to $\Lambda$CDM (horizontal dashed black). We use the CMB+BAO+SN best-fit parameter values for each model. Black dots represent the DESI DR2 residuals. In gray are $D_V(z)/z_d$ values derived from the $D_M(z)/z_d$ and $D_H(z)/z_d$ actual data points.
• Figure 5: Distance moduli $\mu(z)$ predicted by $\xi\phi$CDM (blue) and $\phi$CDM (orange) relative to $\Lambda$CDM (horizontal dashed black). We use the CMB+BAO+SN best-fit parameter values for each model. 39 out of the total 1829 redshift values in the DESY5 data are duplicated. To construct the blue and orange curves, a small shift $\Delta z=5\times 10^{-8}$ was added to those points to allow interpolation. Black dots represent the DESY5 binned residuals and vertical dotted lines mark bin edges. The DESY5 data have been calibrated by subtracting the inverse-covariance weighted mean.