Does the detection of primordial gravitational waves exclude low energy inflation?

We show that a detectable tensor-to-scalar ratio $(r\ge 10^{-3})$ on the CMB scale can be generated even during extremely low energy inflation which saturates the BBN bound $\rho_{\rm inf}\approx (30 {\rm MeV})^4$. The source of the gravitational waves is not quantum fluctuations of graviton but those of $SU(2)$ gauge fields, energetically supported by coupled axion fields. The curvature perturbation, the backreaction effect and the validity of perturbative treatment are carefully checked. Our result indicates that measuring $r$ alone does not immediately fix the inflationary energy scale.Comment: 6 pages, 3 figure

Stochastic dynamics of multi-waterfall hybrid inflation and formation of primordial black holes

We show that a hybrid inflation model with multiple waterfall fields can result in the formation of primordial black hole (PBH) with an astrophysical size, by using an advanced algorithm to follow the stochastic dynamics of the waterfall fields. This is in contrast to the case with a single waterfall field, where the wavelength of density perturbations is usually too short to form PBHs of the astrophysical scale (or otherwise PBH are overproduced and the model is ruled out) unless the inflaton potential is tuned. In particular, we demonstrate that PBHs with masses of order $10^{20}\, {\rm g}$ can form after hybrid inflation consistently with other cosmological observations if the number of waterfall fields is about 5 for the case of instantaneous reheating. Observable gravitational waves are produced from the second-order effect of large curvature perturbations as well as from the dynamics of texture or global defects that form after the waterfall phase transition.Comment: 23 pages, 5 figure

On the primordial black hole formation in hybrid inflation

We revisit the scenario of primordial black hole (PBH) formation from large curvature perturbations generated during the waterfall phase transition in hybrid inflation models. In a minimal setup considered in the literature, the mass and abundance of PBHs are correlated and astrophysical size PBHs tend to be overproduced. This is because a longer length scale for curvature perturbations (or a larger PBH mass) requires a longer waterfall regime with a flatter potential, which results in overproduction of curvature perturbations. However, in this paper, we discuss that the higher-dimensional terms for the inflaton potential affect the dynamics during the waterfall phase transition and show that astrophysical size PHBs of order $10^{17\text{--}23} \, {\rm g}$ (which can explain the whole dark matter) can form in some parameter space consistently with any existing constraints. The scenario can be tested by observing the induced gravitational waves from scalar perturbations by future gravitational wave experiments, such as LISA.Comment: 14 pages, 8 figures; v2: minor corrections, figures updated, conclusions unchange

Squeezed bispectrum and one-loop corrections in transient constant-roll inflation

In canonical single-field inflation, the production of primordial black holes (PBH) requires a transient violation of the slow-roll condition. The transient ultra slow-roll inflation is an example of such scenario, and more generally, one can consider the transient constant-roll inflation. We investigate the squeezed bispectrum in the transient constant-roll inflation, and find that the Maldacena's consistency relation holds for a sufficiently long-wavelength mode, whereas it is violated for modes around the peak scale for the non-attractor case. We also demonstrate how the one-loop corrections are modified compared to the case of the transient ultra slow-roll inflation, focusing on representative one-loop terms orgiginating from a time derivative of the second slow-roll parameter in the cubic action. We find that the perturbativity requirement on those terms does not rule out the production of PBH from the transient constant-roll inflation. Therefore, it is a simple counterexample of the recently claimed no-go theorem of PBH production from single-field inflation.Comment: 26 pages, 14 figure