Assess local-gravity and matter-era viability of the Rényi reconstruction

Determine whether the Rényi entropy reconstruction on the maximally symmetric branch satisfies the local-gravity and matter-era constraints required for a fully viable infrared modification, including analysis of its scalaron on a cosmological background and incorporation of the matter sector.

Background

The paper establishes that the Rényi entropy reconstruction on the maximally symmetric branch is Dolgov–Kawasaki stable and has a non-tachyonic scalaron for positive deformation parameter. However, these results concern constant-curvature backgrounds and do not address the phenomenological requirements of a viable infrared-modified gravity theory. In particular, compatibility with local-gravity tests and the matter-dominated cosmological era requires analyzing the matter sector and the scalaron on a dynamical cosmological background.

References

Whether it also satisfies the local-gravity and matter-era constraints required for a fully viable infrared modification is a separate issue, requiring the matter sector and the analysis of the scalaron on a cosmological background. This investigation lies beyond the scope of the present work.

— Reconstructing $f(R)$ gravity from generalized entropies: exact Lagrangians  (2608.25722 - Anand et al., 26 Aug 2026) in Section 3.2, “Extensivity, stability and infrared structure”