  We study correlation properties of the generalized elastic model which
accounts for the dynamics of polymers, membranes, surfaces and fluctuating
interfaces, among others. We develop a theoretical framework which leads to the
emergence of universal scaling laws for systems starting from thermal
(equilibrium) or non-thermal (non-equilibrium) initial conditions. Our analysis
incorporates and broadens previous results such as observables' double scaling
regimes, (super)roughening and anomalous diffusion, and furnishes a new scaling
behavior for correlation functions at small times (long distances). We discuss
ageing and ergodic properties of the generalized elastic model in
non-equilibrium conditions, providing a comparison with the situation occurring
in continuous time random walk. Our analysis also allows to assess which
observable is able to distinguish whether the system is in or far from
equilibrium conditions in an experimental set-up.
