Photons and Gravitons as Goldstone Bosons , and the Cosmological Constant

We reexamine a scenario in which photons and gravitons arise as Goldstone bosons associated with the spontaneous breaking of Lorentz invariance. We study the emergence of Lorentz invariant low energy physics in an effective field theory framework, with non-Lorentz invariant effects arising from radiative corrections and higher order interactions. Spontaneous breaking of the Lorentz group also leads to additional exotic but weakly coupled Goldstone bosons, whose dispersion relations we compute. The usual cosmological constant problem is absent in this context: being a Goldstone boson, the graviton can never develop a potential, and the existence of a flat spacetime solution to the field equations is Massless particles can arise by a variety of mechanisms: gauge symmetry, chiral symmetry , supersymmetry, and the spontaneous breaking of global symmetry. The mass-lessness of the photon and graviton is typically associated with the existence of gauge symmetry; here we explore an alternative option in which it is associated with the spontaneous breaking of Lorentz invariance, with the " gauge " fields arising as Goldstone bosons. At the level of low energy effective field theory, the usual argument in favor of exact gauge invariance is based on Lorentz invariance. Some form of gauge invariance is required in order to obtain an interacting, unitary, Lorentz invariant theory of massless particles with spin 1 or 2. In a manifestly Lorentz invariant formulation a violation of gauge invari-ance will typically imply a noncancellation of timelike and longitudinal modes, yielding a non-unitary S-matrix in the physical sector. In a noncovariant gauge fixed formulation unitarity is manifest, but the action is required to be formally gauge invariant in order to recover Lorentz invariance of the S-matrix. Especially in the case of gravity, there are various motivations for exploring alternatives. First, it is a basic fact that we inhabit a universe that is not Lorentz invariant at large scales due to cosmological expansion. Second, in the case of gravity gauge invariance is insufficient to guarantee masslessness, since a potential Λ 4 √ −g is allowed. Since a nonzero cosmological constant leads to a non-Lorentz invariant vacuum, the original motivation for gauge invariance is not actually realized. As an alternative we turn to effective actions that yield massless photons and gravitons as Goldstone bosons of spontaneously broken Lorentz invariance. Of course, the effective theory must be consistent with the observed accuracy of Lorentz invariance at distances small compared to the curvature scale of …