For f(R)=R+αR^n, the dual scalar-tensor potential is bounded below with a minimum exactly for even n and positive α, matching the f''(R)>0 condition.
Linearized f (r) gravity: gravitational radiation and solar system tests
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Does the stability of f(R) theories imply the stability of the dual scalar-tensor theory ?
For f(R)=R+αR^n, the dual scalar-tensor potential is bounded below with a minimum exactly for even n and positive α, matching the f''(R)>0 condition.