The project will study a large variety of non-equilibrium dynamics and relaxation in a strongly correlated quantum systems. The starting point of our investigations is a quantum simulation of the Sine-Gordon model via two tunnel-coupled 1D superfluids. In the experiments we can tune the physics form simple gaussian to very strongly correlated. We will investigate (i) relaxation after quenches; (ii) design specific dynamical driving of the SG model to (ii.a) prepare the SG QuFT close to its quantum vacuum state and (ii.b) build a model of an expanding universe; (iii) study strong excitations and particle creation, thereby we can create starting conditions which will be outside the validity of the implementation of the SG model and study the range of validity of the quantum simulator; and (iv) study the non-equilibrium dynamics in spatially inhomogeneous systems like the boundary SG model. Central to all these investigations will be to verify the model and to probe its range of validity.