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Modulated Ground State of Gravity Theories with Stabilized Conformal Factor

We discuss the stabilization of the conformal factor by higher derivative terms in a conformally reduced $R+R^2$ Euclidean gravity theory. The flat spacetime is unstable towards the condensation of modes with nonzero momentum, and they "condense" in a modulated phase above a critical value of the coupling $β$ of the $R^2$ term. By employing a combination of variational, numerical and lattice methods we show that in the semiclassical limit the corresponding functional integral is dominated by a single nonlinear plane wave of frequency $\approx 1/\sqrtβ \lp$. We argue that the ground state of the theory is characterized by a spontaneous breaking of translational invariance at Planckian scales.