Primordial density perturbation and decaying speed of sound

The decaying speed of sound can lead to the emergence of the primordial density perturbation in any expanding phase, even if the expansion is decelerated. Recently, some proposals have been given to implement this mechanism, in which it was found that the primordial spectrum of scalar perturbation can be scale invariant. In this paper, we will give more insights for the details of this seeding mechanism.