Cosmic structures in Ricci-inverse theories of gravity

We discuss a no-go theorem for the novel Ricci-inverse theory of modified gravity. By considering a static spherically symmetric matter distribution embedded within a de Sitter cosmology, we demonstrate that achieving a stable Sub-Horizon non-relativistic Weak-Field limit is unattainable in any of the models previously proposed to mitigate certain cosmological and inflationary instabilities. We explore potential strategies to address this challenge, suggesting a novel methodology for constructing stable models that adhere to the Sub-Horizon non-relativistic Weak-Field limit. These models are shown to maintain full consistency with the predictions of General Relativity at small scales.