Constraining the New Aether: Gravitational Cherenkov Radiation

TL;DR

The paper analyzes spontaneous Lorentz violation in the New Aether theory, where a fixed-modulus vector field $S^ u$ couples to gravity and yields five propagating modes whose speeds depend on the coefficients $c_i$. By computing gravitational Cherenkov radiation and the associated energy loss of ultra-high-energy cosmic rays, the authors derive stringent bounds on combinations of the $c_i$ and on the scale of Lorentz violation, $v$, including $rac{-igl(c_1+c_3igr)}{2} < 5 imes 10^{-16}$ and other tight constraints on $(c_1,c_2,c_3,c_4)$. They show that, unless the theory lies on a narrow nearly-luminal subspace or the Lorentz-violating scale is extremely small, the $c_i$ must be smaller than $oxed{10^{-15}}$, providing the strongest tests to date of spontaneous Lorentz violation in gravity. The analysis accounts for all five modes (two gravitons, three $S$ modes) and includes detailed kinematics and matrix-element calculations for processes such as $ ext{graviton} o$ emission of $S$-modes and off-shell graviton-mediated $ ext{ψ} o ext{ψ}SS$ transitions, highlighting the role of spin and dispersion in shaping the constraints.

Abstract

We study the simplest concrete theory for spontaneous Lorentz violation, the ``New Aether Theory'' of Jacobson and Mattingly, which is a vector-tensor gravitational theory with a fixed-modulus condition on the vector field. We show that the observation of ultra-high energy cosmic rays (which implies the absence of energy loss via various Cherenkov type processes) places constraints on the parameters of this theory, which are much stronger than those previously found in the literature and are also stronger than the constraints generically arising when gravity displays sub-luminal propagation.