Particle production from inhomogeneities: general metric perturbations

We present universal formulas for particle production from gravitational inhomogeneities. In the massless limit the result is strikingly simple and completely determined by the two-point function of the energy-momentum tensor that is fixed up to a constant - the central charge - for conformally coupled scalars, massless fermions and gauge fields. This result can be applied to any conformally coupled theory, weakly or strongly interacting, unifying previous derivations for fields of different spin and for scalar and tensor perturbations. We derive the results using the Schwinger method of 1PI effective action and through Bogoliubov transformations that allows to compute exclusive information on the distribution of particles. We then apply these results to stochastic backgrounds of scalar and tensor perturbations that can be generated by various phenomena such us inflationary perturbations and first order phase transitions. Differently from particle production usually considered in cosmology this mechanism allows for the production of massless fields. In particular the abundance induced by inhomogeneities can easily reproduce the dark matter abundance if scalar perturbations produced from inflation are enhanced at short scales.