Dynamical dark energy in the no-scale Brans-Dicke gravity

TL;DR

This work embeds a quintessence field within a no-scale Brans--Dicke gravity by introducing a second scalar with an O($2$) symmetry and breaking it down to a $D_4$ subgroup, producing a cosine-type quintessence potential with a decay constant $f_a = M_{\text{Pl}}/(4\sqrt{\xi})$. By further incorporating an $R^2$ term and a non-minimal Higgs coupling, the model naturally yields an inflationary sector with a plateau driven by the field $\Theta$, while preserving a dynamical quintessence sector that attains a super-Planckian $f_a$ for small $\xi$ (e.g., $\xi \lesssim 10^{-3}$). The construction aligns with recent DESI DR2 findings that permit $f_a$ near or above the Planck scale, providing a gravity-sector origin for dynamical dark energy. The authors also discuss possible extensions to an SO($3$) symmetry that could realize two light scalar degrees of freedom, enabling scenarios with two quintessence fields or a light DM component coupled to dark energy. Overall, the paper links late-time acceleration to gravitational-sector dynamics and demonstrates a concrete pathway to super-Planckian quintessence within a no-scale framework.

Abstract

We add a new scalar field in the no-scale Brans-Dicke gravity and require it to have a global O(2) symmetry with the original scalar field in the Brans-Dicke gravity. This gives us a new massless scalar field in the Einstein frame due to the SO(2) symmetry. We then explicitly break the O(2) symmetry to a $D_4$ symmetry, and this scalar field gains a periodic potential. This scalar field can serve as the quintessence field to explain dark energy. If we further add the $R^2$ term and the non-minimal coupling to the Higgs field, we can realize inflation and reheating, and this leads to a super-Planckian decay constant of the quintessence potential. The super-Planckian decay constant is consistent with the newly released observational data according to a recent analysis.