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We consider gravitational perturbation around maximally symmetric backgroundof a theory of gravity involving quadratic curvature correction. This leads toa decoupled model of the standard transverse, traceless graviton mode and anadditional scalar degree of freedom. Evolution of the latter is governed by aLagrangian, which depends on higher derivative terms, inherited from thequadratic curvature correction in the action. It turns out that stability ofthe gravitational theory allows the scalar sector to choose between possiblelowest energy states (or, ground states), that can sustain periodic form ofinhomogeneity, either in space or in time. The latter, with a restricted formof invariance in time translation, is possibly a variant form of the timecrystal. Existence of this novel ground state, depicting a time crystal, issolely related to the presence of higher curvature terms in the action. Inparticular, this non-trivial condensate-like ground state describe thespacetime fabric itself by introducing fundamental scales in the theory.Possible implications are also discussed.

Non-trivial time crystal-like ground state for gravitational perturbation in quadratic gravity