Abstract: We present an overview on the current research in the field of analogue models of gravity, and introduce exciting recent results on the back-reaction problem. The problem of the back-reaction plunges its roots in the field of gravity but, nevertheless, is a general concept, and relevant to a wide range of physical systems. It aims towards a self-consistent theory of the interaction between quantum fields and their background, that in the case of gravity is represented by spacetime. While at the kinematic (test field) level we observe the excitation of real particles out of the vacuum state of a field, that is driven by a background that is non-stationary (cosmological particle creation) or endowed with a non-trivial topological structure (Hawking radiation emanated from a black hole), the back-reaction problem addresses the quest of how the excited particles affect the dynamics of the background itself.

We present recent work on the back-reaction within the framework of optomechanics and analogue models of gravity. In the former case, the non-trivial background experienced by the electromagnetic field is encoded in the boundary conditions provided by the mechanical degrees-of-freedom (mirrors) in these systems. The back-reaction here is due by the dynamical Casimir emission, which affects the motion of the mirrors. In the latter case, we use a Bose-Einstein condensates of ultra-cold atoms as a quantum simulator of the Pre-Heating in the early Universe. This is the process by which matter in the Universe is created out of the fluctuations of the inflaton field, which drives the primordial expansion of the Universe, that is the inflation. In both cases, we show that non-equilibrium quantum fields processes affect the dynamics of the background by inducing dissipation, fluctuations and de-coherence.

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