Beyond Growth-only Modified Gravity: Background Dynamics in Information-Based Gravity

We present a conceptual extension beyond growth-only modified gravity models,motivated by information-based emergent gravity scenarios. While growth-onlyimplementations provide a clean and controlled limit with a fixed ΛCDMbackground, a complete realization of information-based gravity is expectedto modify both background expansion and structure growth. In this work we outline a minimal and internally consistent framework in whichbackground and perturbation-level modifications arise from a commoninformational origin. No specific functional form or numerical implementationis assumed. The purpose of this paper is to provide a conceptual roadmapbridging controlled growth-only studies and fully dynamical background-plus-growth modified gravity models.