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A fundamental criterion of viability of any gravity theory is existence of astable ground-state solution being either Minkowski, dS or AdS space. Stabilityof the ground state is independent of which frame is physical. In general, agiven theory has multiple ground states and splits into independent physicalsectors. All metric gravity theories with the Lagrangian being a function ofRicci tensor are dynamically equivalent to Einstein gravity with a source andthis allows us to study the stability problem using methods developed in GR. Weapply these methods to f(R) theories. As is shown in 13 cases of Lagrangiansthe stability criterion works simply and effectively whenever the curvature ofthe ground state is determined. An infinite number of gravity theories have astable ground state and further viability criteria are necessary.

Metric gravity theories and cosmology:II. Stability of a ground state in f(R) theories