Production Of Gravitational Waves During Preheating In The Starobinsky Inflationary Model

Inflation,a phase of quasi-exponential expansion in the early universe,can resolve most of theoretical problems in the big bang standard cosmology.Fur-thermore,the scalar quantum fluctuations during inflation provide the seed for the formation of large scale structure.Inflation usually is driven by a slow-roll single scalar field,which predicts a scale-invariant spectrum of scalar fluctuations on the super-horizon scale.This prediction is consistent with the Cosmic Microwave Back-ground(CMB)observations.Except for the scalar perturbations,there also exists the tensor fluctuations during inflation,which is also scale-invariant on large scales.Since the tensor perturbations lead to the B-mode polarization for the CMB photon,its amplitude can be constrained by the CMB observations.The Starobinsky model is now regarded as one of the most popular inflationary models due to its great consistency with CMB observations.After inflation,the universe enters the stage of reheating.In this stage,the energy of the inflaton is transformed into the basic particles,bringing the universe to a period dominated by radiation.Preheating is the first stage of reheating,during which the inflaton usually will undergo a period-ical oscillation around the minimum of its potential.And the periodical oscillation of the inflaton may lead to an explosive production of the inflaton quanta or other light particles coupled to the inflation field through the parametric resonance.When the mode momenta of the inflaton quanta or the light fields are in the resonance bands,these modes will grow exponentially,but the others don't grow.Since on-ly a part of modes have the resonant momenta,the matter distribution has large inhomogeneities in the position space,which becomes an effective source to emit gravitational waves(GWs).The production of GWs during preheating in the Starobinsky model with a nonminimally coupled auxiliary scalar field is studied through the lattice simulation in this paper.We find that the GWs spectrum ?gw grows fast with the increase of the absolute value of coupling parameter?.This is because the resonant bands become broad and preheating becomes more effective with the increase of |?|.When?<0,?gw begins to grow once the inflation ends and grows faster than the case of ?>0.?gw reaches the maximum at ?=-20(?=42 for the case ?>0)and then decreases with slight oscillation.Finally,we find that gravitational waves at low frequencies decay more slowly than at high frequencies,which may result in very strong low-frequency modes in the gravitational wave background today.Furthermore we find that the GWs produced in the era of preheating satisfy the limits from the Planck and next-generation CMB experiments.