Defect-antidefect correlations in a lyotropic liquid crystal from a cosmological point of view

In this work, we analyze the defect and antidefect distribution in the nematic calamitic phase of a lyotropic liquid crystal [the ternary mixture formed by potassium laurate (KL), decanol (DeOH), and water]. We obtain defects with wedge disclinations of strength +/- 1/2, and the scaling exponent determined by the defect-antidefect correlation was 0.29 +/- 0.07. This value is in good agreement with the theoretical value of 1/4 obtained by the Kibble mechanism. The constant of the scaling relation of the defect and antidefect distribution is also discussed. We compare our results with the values obtained by Digal [Phys. Rev. Lett. 83, 5030 (1999)] who used a thermotropic liquid crystal.