Analogue spacetimes: Toy models for "quantum gravity''

Why are "analogue spacetimes'' interesting? For the purposes of this workshop the answer is simple: Analogue spacetimes provide one with physically well-defined and physically well-understood concrete models of many of the phenomena that seem to be part of the yet incomplete theory of "quantum gravity'', or more accessibly, "quantum gravity phenomenology''. Indeed "analogue spacetimes'' provide one with concrete models of "emergence'' (whereby the effective low-energy theory can be radically different from the high-energy microphysics). They also provide many concrete and controlled models of "Lorentz symmetry breaking'', and extensions of the usual notions of pseudo-Riemannian geometry such as "rainbow spacetimes'', and pseudo-Finsler geometries, and more. I will provide an overview of the key items of "unusual physics'' that arise in analogue spacetimes, and argue that they provide us with hints of what we should be looking for in any putative theory of "quantum gravity''. For example: The dispersion relations that naturally arise in the known emergent/analogue spacetimes typically violate analogue Lorentz invariance at high energy, but do not do so in completely arbitrary manner. This suggests that a search for arbitrary violations of Lorentz invariance is possibly overkill: There are a number of natural and physically well-motivated restrictions one can put on emergent/ analogue dispersion relations, considerably reducing the plausible parameter space.