Einstein aether theory

Einstein-aether theories were popularized by Maurizio Gasperini in a series of papers, such as Singularity Prevention and Broken Lorentz Symmetry in the 1980s.[1] In addition to the metric of general relativity these theories also included a scalar field which intuitively corresponded to a universal notion of time. Such a theory will have a preferred reference frame, that in which the universal time is the actual time. The dynamics of the scalar field is identified with that of an aether which is at rest in the preferred frame. This is the origin of the name of the theory, it contains Einstein's gravity plus an aether.

Einstein aether theories returned to prominence at the turn of the century with the paper Gravity and a Preferred Frame by Ted Jacobson and David Mattingly.[2] Their theory contains less information than that of Gasperini, instead of a scalar field giving a universal time it contains only a unit vector field which gives the direction of time. Thus observers who follow the aether at different points will not necessarily age at the same rate in the Jacobson–Mattingly theory.

The existence of a preferred, dynamical time vector breaks the Lorentz symmetry of the theory, more precisely it breaks the invariance under boosts. This symmetry breaking may lead to a Higgs mechanism for the graviton which would alter long distance physics, perhaps yielding an explanation for recent supernova data which would otherwise be explained by a cosmological constant. The effect of breaking Lorentz invariance on quantum field theory has a long history leading back at least to the work of Markus Fierz and Wolfgang Pauli in 1939. Recently it has regained popularity with, for example, the paper Effective Field Theory for Massive Gravitons and Gravity in Theory Space by Nima Arkani-Hamed, Howard Georgi and Matthew Schwartz.[3] Einstein-aether theories provide a concrete example of a theory with broken Lorentz invariance and so have proven to be a natural setting for such investigations. In 2004, Eling, Jacobson and Mattingly wrote a review of the status Einstein aether theory as of 2004.[4]

The action of the Einstein aether theory is generally taken to consist of the sum of the Einstein–Hilbert action with a Lagrange multiplier λ that ensures that the time vector is a unit vector and also with all of the covariant terms involving the time vector u but having at most two derivatives.

In particular it is assumed that the action may be written as the integral of a local Lagrangian density

${\displaystyle S={\frac {1}{16\pi G_{N}}}\int d^{4}x{\sqrt {-g}}{\mathcal {L}}}$

where G_N is Newton's constant and g is a metric with Minkowski signature. The Lagrangian density is

${\displaystyle {\mathcal {L}}=-R-K_{mn}^{ab}\nabla _{a}u^{m}\nabla _{b}u^{n}-\lambda (g_{ab}u^{a}u^{b}-1).}$

Here R is the Ricci scalar, ${\displaystyle \nabla }$ is the covariant derivative and the tensor K is defined by

${\displaystyle K_{mn}^{ab}=c_{1}g^{ab}g_{mn}+c_{2}\delta _{m}^{a}\delta _{n}^{b}+c_{3}\delta _{n}^{a}\delta _{m}^{b}+c_{4}u^{a}u^{b}g_{mn}.}$

Here the c_i are dimensionless adjustable parameters of the theory.

In Universal Dynamics of Spontaneous Lorentz Violation and a New Spin-Dependent Inverse-Square Law Force Nima Arkani-Hamed, Hsin-Chia Cheng, Markus Luty and Jesse Thaler have examined experimental consequences of the breaking of boost symmetries inherent in aether theories. They have found that the resulting Goldstone boson leads to, among other things, a new kind of Cherenkov radiation.

In addition they have argued that spin sources will interact via a new inverse square law force with a very unusual angular dependence. They suggest that the discovery of such a force would be very strong evidence for an aether theory, although not necessarily that of Jacobson, et al.

• Aether theories
• Modern searches for Lorentz violation

• Einstein aether theory on arxiv.org