### 7.11 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 [435, 321]. 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 [360, 182] to brane worlds [99] and loop quantum gravity [229]. 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, [6, 141, 318, 317, 319, 320, 321, 435, 579, 396] 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, an 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 with new ideas
about other effects of physical quantum gravity that might be observable at sub-Planckian
energies.