Following a new microlensing constraint on primordial black holes (PBHs) with $\sim 10^{20}–10^{28}\mathrm{g}$ [H. Niikura et al., arXiv:1701.02151.], 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 $\simeq 10^{20}\mathrm{g}$ with a small width $\sigma \lesssim 0.1$, 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 that 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 puts severe restriction on its $\mu$ distortion. In particular, it is found that the scalar power spectrum should have a very sharp peak at $k\sim 10^6{\mathrm{Mpc}}^{-1}$ to fulfill the required abundance of PBHs while evading constraints from the PTA experiments together with the $\mu$ distortion. We propose a mechanism that can realize such a sharp peak. In the future, simple inflation models that generate PBHs via almost Gaussian fluctuations could be probed/excluded.

We propose a novel scenario to produce abundant primordial black holes (PBHs) in new inflation which is a second phase of a double inflation in the supergravity framework. In our model, some preinflation phase before the new inflation is assumed and it would be responsible for the primordial curvature perturbations on the cosmic microwave background scale, while the new inflation produces only the small scale perturbations. Our new inflation model has linear, quadratic, and cubic terms in its potential and PBH production corresponds with its flat inflection point. The linear term can be interpreted to come from a supersymmetry-breaking sector, and with this assumption, the vanishing cosmological constant condition after inflation and the flatness condition for the inflection point can be consistently satisfied.

There has been a growing evidence for the existence of magnetic fields in the extra-galactic regions, while the attempt to associate their origin with the inflationary epoch alone has been found extremely challenging. We therefore take into account the consistent post-inflationary evolution of the magnetic fields that are originated from vacuum fluctuations during inflation. In the model of our interest, the electromagnetic (EM) field is coupled to a pseudo-scalar inflaton through the characteristic term F, breaking the conformal invariance. This interaction dynamically breaks the parity and enables a continuous production of only one of the polarization states of the EM field through tachyonic instability. The produced magnetic fields are thus helical. We find that the dominant contribution to the observed magnetic fields in this model comes from the modes that leave the horizon near the end of inflation, further enhanced by the tachyonic instability right after the end of inflation. The EM field is subsequently amplified by parametric resonance during the period of inflaton oscillation. Once the thermal plasma is formed (reheating), the produced helical magnetic fields undergo a turbulent process called inverse cascade, which shifts their peak correlation scales from smaller to larger scales. We consistently take all these effects into account within the regime where the perturbation of is negligible and obtain Beff ~ 10−19 G, indicating the necessity of additional mechanisms to accommodate the observations.

We propose a new approach for calculating the curvature perturbations produced during inflation in the stochastic formalism. In our formalism, the fluctuations of the e-foldings are directly calculated without perturbatively expanding the inflaton field and they are connected to the curvature perturbations by the δN formalism. The result automatically includes the contributions of the higher order perturbations because we solve the equation of motion non-perturbatively. In this paper, we analytically prove that our result (the power spectrum and the nonlinearity parameter) is consistent with the standard result in single field slow-roll inflation. We also describe the algorithm for numerical calculations of the curvature perturbations in more general inflation models.

The recent result of the Dark Energy Spectroscopic Instrument (DESI) in combination with other cosmological data shows evidence of the evolving dark energy parametrized by the $w_0{w}_a\mathrm{CDM}$ model. We interpret this result in terms of a quintessential scalar field and demonstrate that it can explain the DESI result even though it becomes eventually phantom in the past. Relaxing the assumption on the functional form of the equation-of-state parameter $w=w(a)$, we also discuss a more realistic quintessential model. The implications of the DESI result for Swampland conjectures, cosmic birefringence, and the fate of the Universe are discussed as well.