### 6.4 Quantum gravity - phenomenology

Over the last few years a widespread consensus has emerged that observational tests of quantum gravity
are for the foreseeable future likely to be limited to precision tests of dispersion relations and their possible
deviations from Lorentz invariance [261]. The key point is that at low energies (well below the Planck
energy) one expects the locally Minkowskian structure of the spacetime manifold to guarantee that one sees
only special relativistic effects; general relativistic effects are negligible at short distances. However as
ultra high energies are approached (although still below Planck scale energies) several quantum
gravity models seem to predict that the locally Euclidean geometry of the spacetime manifold
will break down. There are several scenarios for the origin of this breakdown ranging from
string theory [214, 109] to brane worlds [54] and loop quantum gravity [134]. Common to
all such scenarios is that the microscopic structure of spacetime is likely to show up in the
form of a violation of Lorentz invariance leading to modified dispersion relations for elementary
particles. Such dispersion relations are characterised by extra terms (with respect to the standard
relativistic form) which are generally expected to be suppressed by powers of the Planck energy.
Remarkably the last years have seen a large wealth of work in testing the effects of such dispersion
relations and in particular strong constraints have been cast by making use of high energy
astrophysics observations (see for example [3, 82, 195, 194, 196, 197, 261, 355] and references
therein).
Several of the analogue models are known to exhibit similar behaviour, with a low-momentum
effective Lorentz invariance eventually breaking down at high momentum once the microphysics is
explored.
Thus some of the analogue models provide controlled theoretical laboratories in which at least some forms
of subtle high-momentum breakdown of Lorentz invariance can be explored. As such the analogue
models provide us with hints as to what sort of modified dispersion relation might be natural to
expect given some general characteristics of the microscopic physics. Hopefully investigation
of appropriate analogue models might be able to illuminate possible mechanisms leading to
this kind of quantum gravity phenomenology, and so might be able to provide us new ideas
about other effects of physical quantum gravity that might be observable at sub-Planckian
energies.