Inflationary Model For The Generation Of Primordial Black Holes And Scalar Induced Gravitational Waves

Primordial black holes can explain not only the gravitational wave events,such as GW 150914,GW190412 and GW190814 et al.,but also the origin of the Planet 9.Additionally,primordial black holes as dark matter candidate attracted lots of attention.In order to obtain the magnitude of the amplitude of power spectrum that can produce significant primordial black hole dark matter to guide us construct inflation model,we constrain the power spectrum of primordial curvature perturbations at small scales from the observations of primordial black holes,and get the upper limit of power spectrum of primordial curvature perturbations,A?(?)0.05,which is 7 orders of magnitude larger than those at small scales.The first order scalar perturbations(primordial curvature perturbations)can be the source of the second order tensor perturbations to induce gravitational waves,namely,scalar induced gravitational waves,due to the mixing of scalar and tensor perturbations.Therefore,the scalar induced gravitational waves are produced accompanied by the generation of primordial black holes.We provide a new semianalytic expression for the calculation of scalar induced gravitational waves in Newton gauge during radiation domination by assuming that the scalar induced gravitational waves are generated after the horizon reentry.In order to compare the difference between scalar induced gravitational waves produced before and after the horizon reentry,we use parametrized power spectrum of primordial curvature perturbations to compute the scalar induced gravitational waves,and find the difference is small.We also discuss the detectability and gauge dependence of scalar induced gravitational waves.In order to produce significant primordial black hole dark matter and observational scalar induced gravitational waves,we propose a new inflation mechanism and explain how this new mechanism works with some concrete models.With the introduction of noncanonical kinetic term with a peak function,the power spectrum of primordial curvature perturbations is enhanced by 7 orders of magnitude at small scales successfully,at the same time,it satisfies the constraints at large scales.We name this model as k/G inflation.We compute the primordial black hole dark matter and scalar induced gravitational waves produced by k/G inflation.k/G inflation can produce different mass range primordial black holes by adjusting model parameters.The produced primordial black holes with the mass about 10-12M?can consist all dark matter;The produced primordial black holes with the Earth's mass can explain the origin of the Planet 9;The primordial black holes with the stellar mass produced by k/G inflation can explain the gravitational wave events observed by Laser Interferometer Gravitational-Wave Observatory.In this dissertation,we generalize our original k/G inflation to produce power spectrum with double peaks at small scales.The generalized k/G inflation can produce two mass-range primordial black holes,which can explain more dark matter in different mass ranges.The scalar induced gravitational waves produced by k/G inflation can be observed by future space based gravitational wave observatory,especially for the model that can produce double peaks,it also produces scalar induced gravitational waves with observational double peaks.The observational primordial black holes and scalar induced gravitational waves can be used to test our k/G model.We also use parameterized power spectrum to analyze the waveform of scalar induced gravitational waves.We get an approximate expression of scalar induced gravitational waves in infrared and ultraviolet regions,the waveform is useful to distinguish the background gravitational waves and to understand the generation mechanism of background gravitational waves.There may be large primordial non-Gaussianity due to the 7 orders of magnitude amplification of the power spectrum.We compute the primordial non-Gaussianity in k/G inflation and discuss the effects of non-Gaussianity on the primordial black hole dark matter abundance and the energy density of scalar induced gravitational waves.Although the nonGaussianity is large at some scales,it's still small at the peak scales we are interested in,so the effects of non-Gaussianity on primordial black hole dark matter abundance and the energy density of scalar induced gravitational waves are negligible.