Non-minimally Coupled Running Curvaton: A Unified Approach to Early-Universe Inflation and Phantom Dark Energy

TL;DR

The paper tackles the tension between DESI's hints of dynamical dark energy crossing the phantom divide and the standard $\Lambda$CDM paradigm. It introduces a unified framework by non-minimally coupling the Running Curvaton to gravity with $\xi\,\chi^2 R$ and a modified potential, enabling a phantom-crossing $w(z)$ while preserving inflation-era predictions through a re-tuning $g_0^{obs}=g_0+2\xi$. Key results include a stable Horndeski-compatible dynamics with $c_s^2=1$, compatibility with Planck observations for $n_s$ and $f_{NL}$, and DESI-consistent $w_0$–$w_a$ trajectories (with $w_0>-1$, $w_a<0$). This approach offers a robust, testable path toward a unified description of the early and late-time universe, with future surveys like Euclid and LSST poised to probe the predicted $w_0$–$w_a$ evolution.

Abstract

Recent observations from the Dark Energy Spectroscopic Instrument (DESI) 2024, combined with CMB and SNIa data, indicate a preference for a dynamical dark energy equation of state that crosses the phantom divide ($w < -1$). This finding challenges the standard $Λ$CDM model and minimally coupled scalar field scenarios, including the original Running Curvaton model, which is typically constrained to the quintessence regime. In this work, we propose a unified cosmological framework by extending the Running Curvaton model via a non-minimal gravitational coupling of the form $ξχ^2 R$. We demonstrate that this geometric modification allows the effective equation of state to naturally evolve from a quintessence-like to a phantom-like regime in the Jordan frame, thereby providing a superior fit to the DESI observational contours ($w_0 > -1, w_a < 0$). Crucially, we show that the introduction of non-minimal coupling does not compromise the model's success in describing the early universe. Through a parameter re-tuning mechanism involving the coupling constant ($g_0^{obs} = g_0 + 2ξ$), the predictions for the primordial power spectrum (spectral index $n_s$) and local-type non-Gaussianity ($f_{NL}$) remain strictly preserved and consistent with Planck data. Furthermore, we perform a comprehensive stability analysis within the Horndeski framework, verifying that the model remains free from ghost and gradient instabilities ($c_s^2 = 1$). Our results suggest that the non-minimally coupled Running Curvaton offers a robust, stable, and unified description of inflation and late-time accelerated expansion compatible with the latest precision cosmology data.

Figures (3)

• Figure 1: The evolution for the equation of state $w(z)$. The blue solid line corresponds $(\xi,\lambda,V_0,V_1)=(2.3,0.75,0.94,5.29)$. The green dashed-dotted line is $(\xi,\lambda,V_0,V_1)=(2.1,1.42,0.72,2.24)$. The red dotted line is $(\xi,\lambda,V_0,V_1)=(3.0,0.5,0.9,5.0)$. The orange dashed line is $(\xi,\lambda,V_0,V_1)=(1.5,0.82,0.65,2.67)$. We have set $M_P=1$ and $\rho_{M,0}=3M_P^2\Omega_m^0=0.93$ with $\Omega_m^0=0.31$ and $H_0=69\rm ~km~s^{-1}~Mpc^{-1}$.
• Figure 2: Observational Constraints vs. Non-minimal Coupling Curvaton. This figure compares the theoretical predictions of our non-minimally coupled Running Curvaton model with the 68% and 95% confidence levels from DESI Y5, Pantheon+, and Union3 datasets. The four distinct models correspond to the four cases in Fig. \ref{['fig:evolution of w']}. The black star corresponds to the $\Lambda CDM$.
• Figure 3: $68\%$ and $95\%$ C.L. posterior distributions for runing curvaton model from from the combination of DESI BAO $+$ Pantheon, obtained from sampling uniformly in the parameters via fig. \ref{['fig:w0_wa_evolution']}.