Measuring cosmic defect correlations in liquid crystals

From the theory of topological defect formation proposed for the early Universe, the so-called Kibble mechanism, it follows that the density correlation functions of defects and antidefects in a given system should be completely determined in terms of a single length scale $\xi ,$ the relevant domain size, which is proportional to the average interdefect separation $r_{\mathrm{av}}.$ Thus, when lengths are expressed in units of $r_{\mathrm{av}},$ these distributions should show universal behavior, depending only on the symmetry of the order parameter and space dimensions. We have verified this prediction by analyzing the distributions of defects and antidefects formed during the isotropic-nematic phase transition in a thin layer in a liquid crystal sample. Our experimental results confirm this prediction and are in reasonable agreement with the results of numerical simulations.