Primordial Black Holes:Formation Mechanism And Astronomical Constraints

This thesis aims to study the primordial black hole(PBH)formation in the infla-tionary Universe,and observational constraints on PBH mass spectrum.Within the Sound Speed Resonance(SSR)mechanism,we focus on the following three aspects:1.applying SSR mechanism to inflaton-curvaton mixed scenario;2.realization of the SSR mechanism in Dirac-Born-Infeld(DBI)inflation model;3.studying the induced gravi-tational waves(IGWs)from the inflationary stage in the SSR mechanism.In addition,we also study the critical collapse mass function of PBHs,and impose constraints on the critical collapse mass function via the Big Bang Nucleosythesis(BBN)observations.1.SSR is a novel mechanism for PBH formation proposed in recent years,the pri-mordial curvature perturbations can be largely amplified by the parametric resonance effect of SSR.In Chapter 3,we apply SSR to the inflaton-curvaton mixed scenario,in contrast to the original mechanism,the sound speed of curvaton fluctuations is assumed to be oscillating during inflation,while inflaton leads to the standard adiabatic perturba-tions.Due to the narrow resonance effect of SSR,the curvaton fluctuations around the characteristic mode are amplified,and thus the entropy perturbations during inflation.Then,the entropy perturbations can convert into primordial curvature perturbations af-ter inflation and before curvaton decays.We calculate the primordial power spectrum in this mixed model,and impose the constraints on model parameter space by using the non-Gaussianity.In contrast to previous works,we find in our model that the contri-bution from curvaton to primordial curvature perturbations can dominate within some parameter region.2.One of the theoretical problems about SSR is the model building.In Chapter 4,we realize SSR mechanism within DBI inflation model.DBI inflation is divided into two parts,the non-oscillating stage and the oscillating stage.In the non-oscillating stage,we solve the inflaton background evolution by the matching condition for sound speed.And we also assume this solution also holds in the oscillating stage,and the oscillating sound speed is realized by perturbing the warp factor,and we yield Hubble parameter and inflaton's potential by using Hamilton-Jacobi formalism.After that,we test the theoretical validity of our model and find that the non-smooth conjunction of sound speed between two stages does not yield manifest effects on the phenomenology of SSR,and the violation of adiabaticity condition of the Mukhanov-Sasaki equation does not affect the comoving curvature perturbation after Hubble crossing in the non-resonant region.Making use of observational data including e-folding number,power spectrum and non-Gaussianity,we derive various cosmological constraints on the pa-rameter space.3.IGWs have attracted a lot of attentions these years,the strong correlation be-tween IGWs and PBH formation make it possible to detect PBHs via GW experiments.In Chapter 5,we study the IGWs from the inflationary stage under the framework of SSR mechanism,especially the GWs induced by the super-horizon modes and sub-horizon modes?We calculate the four-point correlation of super-horizon source and then obtain the power spectrum of IGWs.For the sub-horizon modes,we perform a semi-classical analysis,i.e.,using the thin-ring approximation for phase space integral and numerically solving the time integral.And we find that the IGWs from the sub-horizon regime dom-inate the inflationary signal.At last,we calculate the energy spectrum of the IGWs and find that the signal from the inflationary stage is comparable with that of the radiation-dominant epoch,so that the total IGW signal possesses double-peak feature,which can be used as a test for SSR mechanism via GW experiments,like SKA,IPTA and LISA.4.The observational constraints on the critical collapse mass function of PBHs is usually thought to be practically indistinguishable with that of the monochromatic mass function.In Chapter 6,we calculate the Hawking photon spectrum radiated from PBHs.For the electromagnetic cascade,we also correct the spectrum for the low-energy photons.And then,we obtain the variation of 3He abundance due to the photodisinte-gration process trigged by Hawking radiation of PBHs.Thus,we impose the constraints on mass spectrum of PBHs with the monochromatic and critical collapse mass function via 3He observations,respectively.Our results show that the constraint on the criti-cal collapse mass function is about one order stringent than that of the monochromatic mass function.We also show the discrepancy between our monochromatic constraints on PBHs with the previous results.