Implications of the scalaron mass condition

Investigate the full implications of imposing the scalaron non-tachyonic condition $m_s^2>0$ on the higher-dimensional $f(R)$ gravity models considered, including their emergent-vacuum and stability parameter spaces.

Background

The paper analyzes ghost-free higher-dimensional $f(R)$ gravity vacua primarily through the criterion $f'(R)>0$. It derives the scalaron mass for perturbations about constant-curvature backgrounds and notes that, in the five-dimensional Starobinsky model under the assumptions studied, the scalaron condition is weaker than the ghost-free condition. However, the abstract explicitly states that the scalaron requirement is not imposed in full across the models considered and leaves a detailed study of its consequences unresolved.

A complete investigation would determine how enforcing $m_s^2>0$, in addition to $f'(R)>0$, modifies the allowed couplings and the existence of stable emergent vacua in the single-term and multi-term polynomial $f(R)$ theories analyzed in arbitrary dimensions.