The acoustic metric can be written as
Following [18, 115, 202, 73, 203] one can take a homogeneous system and a radial profile for the velocity , with a scale factor depending only on . Then, defining a new radial coordinate as the metric can be expressed as
The other avenue starts from a fluid at rest with respect to the laboratory at all times:[17, 18]). This again reproduces an expanding flat FLRW Universe.
Models considered to date focus on variants of the BEC-inspired analogues:
In all of these models the general expectations of the relativity community have been borne out - theory definitely predicts particle production, and the very interesting question is the extent to which the formal predictions are going to be modified when working with real systems experimentally . We expect that these analogue models provide us with new insights as to how their inherent modified dispersion relations affect cosmological processes such as the generation of a primordial spectrum of perturbations (see for example [42, 41, 43, 44, 45, 46, 47, 70, 107, 158, 177, 178, 207], [229, 230, 244, 252, 249, 250, 251, 274, 275, 296, 349, 361, 362, 363, 371] where analogue-like ideas are applied to cosmological inflation).
An interesting side-effect of the original investigation, is that birefringence can now be used to model “variable speed of light” (VSL) geometries [28, 108]. Since analogue models quite often lead to two or more “excitation cones”, rather than one, it is quite easy to obtain a bimetric or multi-metric model. If one of these metrics is interpreted as the “gravitational” metric and the other as the “photon” metric, then VSL cosmologies can be given a mathematically well-defined and precise meaning [28, 108].
© Max Planck Society and the author(s)