The acoustic metric can be written as

Essentially there are two ways to use this metric to reproduce cosmological spacetimes: One is based on physical explosion, the other on rapid variations in the “effective speed of light”.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

Introducing a Hubble-like parameter, the equation of continuity can be written as with constant. Finally we arrive at the metric of a flat FLRW geometry with The proper Friedmann time, , is related to the laboratory time, , byThe other avenue starts from a fluid at rest with respect to the laboratory at all times:

Now it is not difficult to imagine a situation in which remains constant, in a sufficiently large region of space, while the speed of sound decreases with time (this can be made in BECs for example by changing with time the value of the scattering length [17, 18]). This again reproduces an expanding flat FLRW Universe.Models considered to date focus on variants of the BEC-inspired analogues:

- Fedichev and Fischer [115, 114] have investigated WKB estimates of the cosmological particle production rate and (1+1) dimensional cosmologies, both in expanding BECs.
- Lidsey [242], and Fedichev and Fischer [116] have focussed on the behaviour of cigar-like condensates in grossly asymmetric traps.
- Barcelo et al. [17, 18] have focussed on the central region of the BEC and thereby tried (at least locally) to mimic FLRW behaviour as closely as possible.
- Fischer and Schützhold [119] propose the use of two-component BECs to simulate cosmic inflation.
- Weinfurtner [425, 424] has concentrated on the approximate simulation of de Sitter spacetimes.

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 [18]. 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].

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