Non-Relativistic Strings in Expanding Spacetime

We obtain a non-relativistic diffeomorphism invariant string action as a special limit of the Nambu-Goto action in an FLRW background. We use this action to study non-relativistic string dynamics in an expanding universe and construct an analytic model describing the macroscopic properties of non-relativistic string networks. The non-relativistic constraint equations allow arbitrarily small string velocities and thus a `frustrated’ equation of state for non-interacting strings can be obtained without the need of a velocity damping mechanism. Assuming that colliding string segments reconnect by exchange of partners, non-relativistic string networks exhibit scaling behaviour, but with enhanced energy densities due to the reduced average string velocity. Non-relativistic string networks can be relevant in several contexts in condensed matter physics and cosmology.