Running spectral index and mode-mode correlation of inflationary perturbations from off-equilibrium effects

We study the off-equilibrium effects of inflaton on the dynamics of primordial perturbations in the O(N) model. A self-consistent off-equilibrium formalism is employed to investigate the evolution of the inflationary background field and its fluctuations with the back-reaction effects. We find two observable remains left behind the off-equilibrium processes: the running spectral index of primordial density perturbations and the correlations between perturbation modes in phase space, which would serve as the imprints to probe the epoch of inflation, even beyond.