The primordial black hole (PBH) formation is studied in light of the inflating curvaton. The typical scale of the PBH formation is determined by curvaton inflation, which may generate PBH with 10 14 g ≤ MPBH ≤ 10 38 g when curvaton inflation gives the number of e-foldings 5 ≤ N2 ≤ 38. The non-Gaussianity of the inflating curvaton does not prevent the PBH formation.

Recent arguments show that some curvaton field may generate the cosmological curvature perturbation. As the curvaton is independent of the inflaton field, there is a hope that the fine-tunings of inflation models can be cured by the curvaton scenario. More recently, however, D.H.Lyth discussed that there is a strong bound for the Hubble parameter during inflation even if one assumes the curvaton scenario. Although the most serious constraint was evaded, the bound seems rather crucial for many models of a low inflation scale. In this paper we try to remove the constraint. We show that the bound is drastically modified if there were multiple stages of inflation.

There are many inflationary models in which inflaton field does not satisfy the slow-roll condition. However, in such models, it is always difficult to generate the curvature perturbation during inflation. Thus, to generate the curvature perturbation, one must introduce another component to the theory. To cite a case, curvatons may generate dominant part of the curvature perturbation after inflation.However, we have a question whether it is unrealistic to consider the generation of the curvature perturbation during inflation without slow-roll. Assuming multi-field inflation, we encounter the generation of the curvature perturbation during inflation

The primordial curvature perturbation ζ may be generated by some curvaton field σ, which is negligible during inflation and has more or less negligible interactions until it decays. In the current scenario, the curvaton starts to oscillate while its energy density ρσ is negligible. We explore the opposite scenario, in which ρσ drives a few e-folds of inflation before the oscillation begins. In this scenario for generating ζ it is exceptionally easy to solve the η problem; one just has to make the curvaton a string axion, with anomaly-mediated susy breaking which may soon be tested at the LHC. The observed spectral index n can be obtained with a potential V ∝ φ p for the first inflation; p = 1 or 2 is allowed by the current uncertainty in n but the improvement in accuracy promised by Planck may rule out p = 1. The predictions include (i) running n ′ ≃ 0.0026 (0.0013) for p = 1 (2) that will probably be observed, (ii) non-gaussianity parameter fNL ∼ −1 that may be observed, (iii) tensor fraction r is probably too small to ever observed.

The Bogoliubov transformation in cosmological particle production can be explained by the Stokes phenomena of the corresponding ordinary differential equation. The calculation becomes very simple as far as the solution is described by a special function. Otherwise, the calculation requires more tactics, where the Exact WKB (EWKB) may be a powerful tool. Using the EWKB, we discuss cosmological particle production focusing on the effect of more general interaction and classical scattering. The classical scattering appears when the corresponding scattering problem of the Schrödinger equation develops classical turning points on the trajectory. The higher process of fermionic preheating is also discussed using the Landau-Zener model.

Topological defects may play the role of the curvatons. We propose a new mechanism of generating density perturbations from cosmological defects in inflationary models. We show several examples in which defects play crucial role in generating density perturbations.

We have studied modulated inflation that generates curvature perturbation from light-field fluctuation. As discussed in previous works, even if the fluctuation of the inflaton itself does not generate the curvature perturbation at the horizon crossing, fluctuation of a light field may induce fluctuation for the end-line of inflation and this may lead to generation of cosmological perturbation "at the end of the inflation". Our scenario is different from those that are based on the fluctuations of the boundary of the inflaton trajectory, as clearly explained in this paper by using the δN formalism. In this paper, we will consider the perturbation of the inflaton velocity that can be induced by a light field other than the inflaton. We also explain the crucial difference from the standard multi-field inflation model. We show concrete examples of the modulated inflation scenario in which non-gaussianity can be generated. We also discuss the running of the non-gaussianity parameter.

A mechanism for generating metric perturbations in inflationary models is considered. Long-wavelength inhomogeneities of light scalar fields in a decoupled sector may give rise to superhorizon fluctuations of couplings and masses in the low-energy effective action. Cosmological phase transitions may then occur that are not simultaneous in space, but occur with time lags in different Hubble patches that arise from the long-wavelength inhomogeneities. Here an interesting model in which cosmological perturbations may be created at the electroweak phase transition is considered. The results show that phase transitions may be a generic source of non-Gaussianity.