  Analogue gravity offers an approach for testing the universality and
robustness of quantum field theories in curved spacetimes and validating them
using down-to-earth, laboratory-based experiments. Fluid interfaces are a
promising framework for creating these gravity simulators and have successfully
replicated phenomena such as Hawking radiation and black hole superradiance.
Recent work has shown that hydrodynamical instabilities on the interface
between two fluids can capture features of the post-inflationary thermalisation
of the Early Universe. In this study, we extend fluid dynamics methods to
develop an effective field theory for the interface between two fluids,
demonstrating the equivalence between the governing equations and a
relativistic scalar field in an analogue spacetime. We also show that the
interfacial height field serves as the analogue relativistic field even in a
nonlinear, interacting field theory. We propose that these mathematical
equivalences can be extrapolated to probe regimes where calculations are
challenging or impractical. Our work provides a new framework for simulating
far-from-equilibrium cosmological and gravitational scenarios in the
laboratory.
