A fast (ca. 3 ms) adiabatic expansion of a volume of liquid He-4 through the lambda transition is being used to study the nature of the transition and to model the cosmological false vacuum to true vacuum phase transition of the early universe. Preliminary results are reported showing that, in accordance with theoretical predictions by W H Zurek (Nature 317, 505; 1985), there is copious production of quantized vortex lines, which represent the superfluid analogue of cosmic strings. The line density after the expansion appears to decay in two distinct stages, with a fast decay being followed by a much slower one, in agreement with earlier work on the decay of quantum turbulence created in thermal counterflow. Extrapolation of the initial fast decay suggests an initial line density, immediately following the expansion, of ca. 10 to power 7 per square cm. Smaller, but still substantial, vortex densities are also found to occur when the system is expanded from below the lambda transition, and the physical implications are discussed.