Primordial Black Holes,Preheating And Primordial Gravitational Waves In Modified Gravity Theories

The super-horizon curvature perturbations generated during inflation not only provide the seed for large scale structure in the Universe but also may lead to the formation of primordial black holes.If the curvature perturbations are large enough,the overdense regions can collapse to form black holes by self-gravitation soon after the horizon entry during the radiation-dominated era.After the end of inflation,the Universe enters a reheating stage,during which the energy of the inflaton is transferred to radiation and the Universe is reheated.In many inflation models,the first stage of reheating is a process called preheating that can lead to the explosive particle production.During this stage,the field fluctuations can grow exponentially via parametric resonanceOn the one hand,the investigations on primordial black holes offer a pos-sibility to resolve the astrophysical and cosmological puzzles,and the curvature perturbations leading to the production of primordial black holes will induce the significant background of gravitational waves which could be detected by future gravitational-wave experiments.Thus,it has important scientific significance for building the inflationary models that enhance the primordial curvature pertur-bations.In present paper,we build this inflationary model in the framework of the nonminimal derivative coupling.On the other hand,the post-inflationary preheating phase can create some potential observational signatures,such as the gravitational wave signals,and the studies on preheating play an important role in understanding the early evolution of the Universe.We discuss the preheating process of the nonminimal coupling inflation model and the Starobinsky inflation model in this paper.We first study the enhancement mechanism of the curvature perturbations in the nonminimal derivative coupling inflation model with a coupling parameter re-lated to the inflaton field.By considering a special form of the coupling parameter as a function of the inflaton,a period of ultra-slow-roll inflation can be realized due to the gravitationally enhanced friction,and the resulting power spectrum of the curvature perturbations has a sharp peak,which is large enough to produce a sizable amount of the primordial black holes and the significant induced gravi-tational wave.We find that the power spectrum of curvature perturbations has a power-law form in the vicinity of the peak.Under this mechanism,we can easily obtain the mass spectrum of primordial black holes around specific masses such as stellar mass,earth mass,and asteroid mass,which can explain the LIGO gravi-tational wave events,the ultrashort-timescale microlensing events in OGLE data,and the most of dark matter,respectively.Meanwhile,we calculate the induced gravitational wave background associated with the primordial black hole forma-tion.We find that the gravitational wave energy spectra can reach the detectable scopes of the future gravitational wave projects.The scaling of the gravitational wave spectrum in the ultraviolet regions is two times that of the power spectrum slope,and has a lower bound.In the infrared regions,the slope of the gravitational wave spectrum can be described roughly by a log-dependent form.These features of the gravitational wave spectrum may be used to check the our mechanism if the induced gravitational waves are detected in the future.Next,we investigate the inflationary dynamics and linear preheating in the nonminimal coupling inflation model in the metric and Palatini formalisms.We find that the value of the inflaton field at the end of the inflation in the Palatini formalism is always larger than that in the metric one,which becomes more and more obvious with the increase of |?|.During the preheating,we find that with the increase of |?|,the resonance bands gradually close to the zero momentum,and the structure of resonance changes and becomes broader and broader in the metric formalism,while it remains to be narrow in the Palatini formalism.The energy transfer from the homogeneous inflaton field to the fluctuation becomes more and more efficient with the increase of |?|,and in the metric formalism the growth of the efficiency of energy transfer is much faster than that in the Palatini formalism.Therefore,the inflation and preheating show different characteristics in different formalisms.Then,we study the nonlinear preheating and the in-process production of gravitational waves in the the nonminimal coupling inflation model in the metric formalism with the method of lattice simulation.We find that the nonminimal coupling enhances the amplitude of the density spectrum of inflaton quanta,and as a result,the peak value of the gravitational wave spectrum generated during preheating is enhanced as well and might reach the limit of detection in future gravitational wave experiments.The gravitational wave spectra in this model exhibit the rich peak structure,and the detection of these peaks in the future will help us to reveal the post-inflationary evolution of the early UniverseFinally,we study the nonlinear preheating after inflation in the Starobinsky model with a nonminimally coupled scalar field ?.Using the lattice simulation,we analyze the rescattering between the,particles and the inflaton condensate,and the backreaction effect of the scalar metric perturbations.We find that the rescattering is an efficient mechanism promoting the growth of the ? field variance Meanwhile,copious inflaton particles can be knocked out of the inflaton conden-sate by rescattering.As a result,the inflaton field can become a non-negligible gravitational wave source,even comparable with the ? field in some parameter regions.For the scalar metric perturbations,which are on the sub-Hubble scale in our analysis,our results show that they have negligible effects on the evolution of scalar fields and the production of gravitational waves in this model.