Modulated Ground State of Gravity Theories with Stabilized Conformal Factor

TL;DR

This paper investigates how higher derivative terms stabilize the conformal factor in gravity theories, revealing a modulated phase with spontaneous translational symmetry breaking at Planckian scales.

Contribution

It demonstrates that in a conformally reduced $R+R^2$ gravity, the conformal factor stabilizes through a modulated phase characterized by a nonlinear plane wave.

Findings

Flat spacetime becomes unstable and condenses into a modulated phase.

The dominant configuration is a nonlinear plane wave with frequency ~1/√β.

Spontaneous breaking of translational invariance occurs at Planckian scales.

Abstract

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 $\beta$ 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 $\approx 1/\sqrt{\beta} \lp$. We argue that the ground state of the theory is characterized by a spontaneous breaking of translational invariance at Planckian scales.