Non-linear Preheating with Scalar Metric Perturbations

We have studied preheating of field perturbations in a 3-dimensional lattice including the effect of scalar metric perturbations, in two generic models of inflation: chaotic inflation with a quartic potential, and standard hybrid inflation. We have prepared the initial state for the classical evolution of the system with vanishing vector and tensor metric perturbations, consistent with the constraint equations, the energy and momentum constraints. The non-linear evolution inevitably generates vector and tensor modes, and this reflects on how well the constraint equations are fulfilled during the evolution. The induced preheating of the scalar metric perturbations is not large enough to backreact onto the fields, but it could affect the evolution of vector and tensor modes. This is the case in hybrid inflation for some values of the coupling $g$ and the height of potential $V_0^{1/4}$. For example with $V_0^{1/4} \simeq 10^{15}$ GeV, preheating of scalar perturbations is such that their source term in the evolution equation of tensor and vector becomes comparable to that of the field anisotropic stress.