Pre-inflationary homogenization of scalar field cosmologies

We consider the evolution of covariant and gauge invariant linear density perturbations of scalar field cosmologies using a dynamical systemsʼ approach. We find conditions for which the perturbations decay in time, so that the spacetime approaches a homogeneous solution which inflates, for quadratic and exponential potentials. This pre-inflationary homogenization is found to be stable in the potentialsʼ parameter spaces. Furthermore, in each case, we determine the minimum size of the resultant homogeneous patch and show that, for quadratic potentials, the resulting inflationary solutions include those with the necessary number of e-folds.