Metric perturbations in a cosmological model with gravitational particle
  production
  The present paper addresses the issue of cosmological metric perturbations in
models of cosmology accompanied by gravitational particle production. The
general structure of such theories is constructed and then the paper focusses
on metric perturbations of the de Sitter space in the early Universe full of
radiation, such spaces can occur in presence of gravitational particle
production. The main focus of the calculations is on scalar metric
perturbations. The paper briefly opines on vector and tensor perturbations of
the de Sitter space in question. The results show that the metric perturbations
can have finite instability in the short scale and these instabilities may
produce the inhomogeneities in the early radiation dominated universe. The
instabilities are in general finite and do not tend to blow up to infinity. The
tensor perturbations do not show any instability in the present model.
