Compared to primordial perturbations on large scales, roughly larger than 1 megaparsec, those on smaller scales are not severely constrained. We revisit the issue of probing small-scale primordial perturbations using gravitational waves (GWs), based on the fact that, when large-amplitude primordial perturbations on small scales exist, GWs with relatively large amplitudes are induced at second order in scalar perturbations, and these induced GWs can be probed by both existing and planned gravitational-wave projects. We use accurate methods to calculate these induced GWs and take into account sensitivities of different experiments to induced GWs carefully, to report existing and expected limits on the small-scale primordial spectrum.

Following a new microlensing constraint on primordial black holes (PBHs) with ∼ 10 20 -10 28 g [1], we revisit the idea of PBH as all Dark Matter (DM). We have shown that the updated observational constraints suggest the viable mass function for PBHs as all DM to have a peak at 10 20 g with a small width σ 0.1, by imposing observational constraints on an extended mass function in a proper way. We have also provided an inflation model that successfully generates PBHs as all DM fulfilling this requirement.

Primordial black holes (PBHs) are one of the candidates to explain the gravitational wave (GW) signals observed by the LIGO detectors. Among several phenomena in the early Universe, cosmic inflation is a major example to generate PBHs from large primordial density perturbations. In this paper, we discuss the possibility to interpret the observed GW events as mergers of PBHs which are produced by cosmic inflation. The primordial curvature perturbation should be large enough to produce a sizable amount of PBHs and thus we have several other probes to test this scenario. We point out that the current pulsar timing array (PTA) experiments already put severe constraints on GWs generated via the second-order effects, and that the observation of the cosmic microwave background (CMB) puts severe restriction on its µ distortion. In particular, it is found that the scalar power spectrum should have a very sharp peak at k ∼ 10 6 Mpc −1to fulfill the required abundance of PBHs while evading constraints from the PTA experiments together with the µ distortion. We propose a mechanism which can realize such a sharp peak. In the future, simple inflation models that generate PBHs via almost Gaussian fluctuations could be probed/excluded.

We study gravitational waves induced from the primordial scalar perturbations at second order around the reheating of the Universe. We consider reheating scenarios in which a transition from an early matter dominated era to the radiation dominated era completes within a timescale much shorter than the Hubble time at that time. We find that an enhanced production of induced gravitational waves occurs just after the reheating transition because of fast oscillations of scalar modes well inside the Hubble horizon. This enhancement mechanism just after an early matterdominated era is much more efficient than a previously known enhancement mechanism during an early matter era, and we show that the induced gravitational waves could be detectable by future observations if the reheating temperature TR is in the range TR 7 × 10 −2 GeV or 20 GeV TR 2 × 10 7 GeV. This is the case even if the scalar perturbations on small scales are not enhanced relative to those on large scales, probed by the observations of the cosmic microwave background.

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A primordial black hole (PBH) is one of the leading nonparticle candidates for dark matter (DM). Although several observations severely constrain the amount of PBHs, it was recently pointed out that there is an uncertainty on the microlensing constraints below ∼10 −10 M ⊙ , which was ignored originally but may weaken the constraints significantly. In this paper, facing this uncertainty, we investigate the possibility that PBHs can make up all DM in a broad mass spectrum. Moreover, we propose a concrete inflation model that can simultaneously produce PBHs for all DM in a broad mass spectrum around Oð10 −13 ÞM ⊙ and PBHs for LIGO events in a sharp mass spectrum at Oð10ÞM ⊙ .

We revisit the effects of an early matter-dominated era on gravitational waves induced by scalar perturbations. We carefully take into account the evolution of the gravita-

Primordial black holes (PBHs) can be produced by the perturbations that exit the horizon during inflationary phase. While inflation models predict the power spectrum of the perturbations in Fourier space, the PBH abundance depends on the probability distribution function (PDF) of density perturbations in real space. In order to estimate the PBH abundance in a given inflation model, we must relate the power spectrum in Fourier space to the PDF in real space by coarse-graining the perturbations with a window function. However, there are uncertainties on what window function should be used, which could change the relation between the PBH abundance and the power spectrum. This is particularly important in considering PBHs with mass 30M that account for the LIGO events because the required power spectrum is severely constrained by the observations. In this paper, we investigate how large influence the uncertainties on the choice of a window function have over the power spectrum required for LIGO PBHs. As a result, it is found that the uncertainties significantly affect the prediction for the stochastic gravitational waves (GWs) induced by the second order effect of the perturbations. In particular, the pulsar timing array constraints on the produced GWs could disappear for the real-space top-hat window function.