Rolling Galileons: Evolving Braiding Strength for Viable Dark Energy

Motivated by growing observational indications that dark energy may be dynamical, we introduce Rolling Galileon gravity: a minimal shift-symmetry-breaking extension of the cubic Galileon in which the coupling coefficients are allowed to vary, giving rise to an evolving braiding strength. The full theory space, shown to be closed under field redefinitions, is characterised by two functions. We derive analytical conditions to satisfy three phenomenological requirements: i) a phantom-crossing equation of state at late times, ii) a positive integrated Sachs-Wolfe signature, and iii) absence of pathologies in the screened scalar force in cosmic voids. We show that these conditions are collectively satisfied by an increasing braiding strength relative to the kinetic sector. A Bayesian analysis of minimal Rolling Galileon models finds that they can satisfy the viability requirements i)-iii) whilst providing an acceptable fit to expansion-history data.