  We construct Carroll-invariant theories with fields propagating outside the
Carroll lightcone, i.e., at a speed strictly greater than zero (`Carroll
swiftons'). We first consider models in flat Carroll spacetime in general
dimensions, where we present scalar and vector Carroll swifton field theories.
We then turn to the coupling to gravity and achieve in particular in two
dimensions a Carroll invariant scalar swifton by coupling it suitably to
Carroll dilaton gravity. Its backreaction on the geometry generates dynamical
torsion.
