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arXiv · 2606.11453

On phase-space singular surfaces in $f(R)$ gravity

Dražen Glavan·David M. J. Vokrouhlický
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Abstract

We perform a Hamiltonian constraint analysis of metric $f(R)$ gravity in the Jordan frame and show that the regular constraint classification degenerates on singular phase-space surfaces located at $f'(R)\!=\!0$ and $f''(R)\!=\!0$. We then study the perturbative implications of these surfaces. For exact backgrounds satisfying $f(R)\!=\!0$ and $f'(R)\!=\!0$, the linearized spectrum is empty; the known pure $R^2$ result is therefore a special case of a more general degeneracy in $f(R)$ gravity. We also show that FLRW trajectories in the Starobinsky model can cross the surface $f'(R)=0$, but that inhomogeneous perturbations develop a degenerate constraint structure at the crossing. The resulting crossing condition is better interpreted as a regularity condition for perturbative evolution than as an ordinary constraint within the Dirac--Bergmann algorithm. Together, these results distinguish backgrounds that lie entirely on a singular surface from backgrounds that cross one dynamically, and show that the two situations lead to different perturbative degeneracies.

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Dražen Glavan, David M. J. Vokrouhlický. 2026-06-09. On phase-space singular surfaces in $f(R)$ gravity. https://arxiv.org/abs/2606.11453

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