Stable Islands of Weak Gravity

We present an exploration of the phenomenology of Horndeski gravity, focusing on regimes that produce weak gravity compared to General Relativity. This letter introduces a novel method to generate models of modified gravity theories that produce a specific observational behaviour while fulfilling stability criteria, without imposing a fixed parametrisation. We start from the inherently stable basis of linear Horndeski theory, implemented in the recently released Einstein-Boltzmann solver mochi_class. The time evolution of the basis functions is designed with Gaussian processes that directly include the stability and phenomenology criteria during the generation. Here, we focus on models with weak gravity that suppress the growth of Large-Scale Structure at late times. To achieve this behaviour, we mainly focus on the design of a dynamical effective Planck mass for theories with a vanishing fifth force. We find a broad range of weak-gravity islands in Horndeski theory space. We also include additional features, like a vanishing modification to gravity at $z=0$, and extend the exploration to islands of gravity with a non-zero fifth force. Finally, we show that replacing the $\mathrm{\Lambda }$CDM expansion model by the DESI $w_0{w}_a$CDM best fit also produces stable islands of weak gravity.