Analytic solutions of scalar perturbations induced by scalar
  perturbations
  We study scalar perturbations induced by scalar perturbations through the
non-linear interaction appearing at second order in perturbations. We derive
analytic solutions of the induced scalar perturbations in a perfect fluid. In
particular, we consider the perturbations in a radiation-dominated era and a
matter-dominated era. With the analytic solutions, we also discuss the power
spectra of the induced perturbations.
