Spontaneous Lorentz Breaking and Massive Gravity

TL;DR

This work develops a bigravity framework with spontaneous Lorentz breaking that yields a consistent massive gravity sector. Two dynamical metrics g1 and g2 interact through a non-derivative potential V(X) depending on X = g1^{-1} g2, admitting both Lorentz-invariant (c = 1) and Lorentz-breaking (c ≠ 1) branches; in the LB phase the tensor sector features a non-diagonal mass mixing between two gravitons, producing a massless mode with v^2 = (1 + c^2 κ)/(1 + κ) and a massive mode with m_g^2 = (1 + κ^{-1}) λ_2 / M_1^2, together with oscillations at high energy. Vectors and scalars do not propagate but mediate static potentials, with a linearly growing term controlled by μ^2 / Δ^2; μ^2 is given by μ^2 = (λ_2/(2 M_1^2)) (λ_μ^2 / λ_η^2), and a non-perturbative Weyl_- symmetry can enforce μ = 0 under δX1 = ε X̄ and 3 λ_4 = - λ_0, yielding a healthy LB phase with nonzero graviton mass. Phenomenology includes time-of-flight differences between gravitons and photons in gravitational wave events, a distance-dependent Newton constant, and potential GW signals from type-2 matter, providing distinctive tests of spontaneous Lorentz breaking massive gravity.

Abstract

We study a theory where the presence of an extra spin-two field coupled to gravity gives rise to a phase with spontaneously broken Lorentz symmetry. In this phase gravity is massive, and the Weak Equivalence Principle is respected. The newtonian potentials are in general modified, but we identify an non-perturbative symmetry that protects them. The gravitational waves sector has a rich phenomenology: sources emit a combination of massless and massive gravitons that propagate with distinct velocities and also oscillate. Since their velocities differ from the speed of light, the time of flight difference between gravitons and photons from a common source could be measured.