Nearly Divergence of Correlation Length and Perturbation Spectrum in String Gas Cosmology

Recently, it has been shown in Ref.[1] that the string thermodynamic fluctuation may lead to a scale invariant spectrum of scalar metric perturbation. However, its realization is still in study. In this note we suppose that the correlation length of metric perturbation, which is proportional to the sound speed, might be nearly divergent at the critical point of phase transition. In this case we find that the string gas mechanism responsible for the generation of primordial perturbation may be applied well.