We study non-Gaussian out-of-equilibrium current fluctuations in a mesoscopic
NSN circuit at the point of a superconducting phase transition. The setup
consists of a voltage-biased thin film nanobridge superconductor (S) connected
to two normal-metal (N) leads by tunnel junctions. We find that above a
critical temperature fluctuations of the superconducting order parameter
associated with the preformed Cooper pairs mediate inelastic electron
scattering that promotes strong current fluctuations. Though the conductance is
suppressed due to the depletion of the quasiparticle density of states, higher
cumulants of current fluctuations are parametrically enhanced. We identify
experimentally relevant transport regime where excess current noise may reach
or even exceed the level of the thermal noise.Comment: 5 pages, 3 figure