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We study, within a framework of the classical fields approximation, thedensity correlations of a weakly interacting expanding Bose gas for the wholerange of temperatures across the Bose-Einstein condensation threshold. We focuson elongated quasi-one-dimensional systems where there is a huge discrepancybetween the existing theory and experimental results (A. Perrin et al., NaturePhys. 8, 195 (2012)). We find that the density correlation function is notreduced for temperatures below the critical one as it is predicted for theideal gas or for a weakly interacting system within the Bogoliubovapproximation. This behavior of the density correlations agrees with the abovementioned experiment with the elongated system. Although the system was muchlarger then studied here we believe that the behavior of the densitycorrelation function found there is quite generic. Our theoretical studiesindicate also large density fluctuations in the trap in the quasicondensateregime where only phase fluctuations were expected. We argue that the enhanceddensity fluctuations can originate in the presence of interactions in thesystem, or more precisely in the existence of spontaneous dark solitons in theelongated gas at thermal equilibrium.

Density fluctuations in a quasi-one-dimensional Bose gas as observed in free expansion