Modified Gravity via Spontaneous Symmetry Breaking

TL;DR

This work constructs a Higgs-like mechanism for gravity by spontaneously breaking local Lorentz invariance with a vector field $A^\mu$ that acquires a vev, producing Lorentz-violating terms in the gravitational action. The linearized theory around a vacuum with $A^\mu=Mn^\mu$ reveals four massless graviton modes, including two GR-like polarizations and two additional Lorentz-violating ones, with dispersion relations that deviate from $k^2=0$ only at $\mathcal{O}(M^2/M_P^2)$; a heavy mode at the scale $M$ decouples. For $\alpha_1<0$, these modes carry positive-definite norms, and the model avoids the van Dam–Veltman–Zakharov discontinuity, recovering GR in the limit $M\to 0$. The UV behavior is controlled with a cut-off $\min(M, M_P)$, and the theory potentially yields observable large-distance effects, offering an alternative to dark energy while remaining compatible with short-distance tests that constrain $M^{-1}$ to be smaller than about $10^{-2}$ cm.

Abstract

We construct effective field theories in which gravity is modified via spontaneous breaking of local Lorentz invariance. This is a gravitational analogue of the Higgs mechanism. These theories possess additional graviton modes and modified dispersion relations. They are manifestly well-behaved in the UV and free of discontinuities of the van Dam-Veltman-Zakharov type, ensuring compatibility with standard tests of gravity. They may have important phenomenological effects on large distance scales, offering an alternative to dark energy. For the case in which the symmetry is broken by a vector field with the wrong sign mass term, we identify four massless graviton modes (all with positive-definite norm for a suitable choice of a parameter) and show the absence of the discontinuity.