Modified Gravity via Spontaneous Symmetry Breaking

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.

Modifying gravity with the aether: An alternative to dark matter

“…It would be interesting to explore the range of current candidates for low energy string theory to find a possible candidate for such an Aether field. What is clear is that a Lagrangian of the form we require will not appear from the standard perturbative approach to constructing effective field theories as in [19]. Non-perturbative effects must come into play.…”

Cosmological attractors in massive gravity

“…Another class of theories with this property is discussed in Refs. [11,12]. In what follows by massive gravity we understand gravity theories (1) obeying symmetry (2).…”

Cosmology of a universe with spontaneously broken Lorentz symmetry

“…This situation is similar to the situation one encounters in higher-derivative theories of gravity. It is not unexpected: in [5], two additional graviton modes are found, a clear indication that we should find more degrees of freedom in this theory than are present in conventional Einstein gravity.…”

“…Recenty, one of us has proposed an action for Einstein gravity coupled with a vector field that leads to modifications to conventional gravitational interactions [5]. The action is constructed strictly according to the rules for an effective field theory with a mass scale cutoff, M : all Lorentz invariant terms containing the vector field and metric up to a predefined order in E/M (where E is the energy scale at which the theory is being considered) are included.…”