Examining the end of inflation with primordial black hole mass distribution and gravitational waves

Abstract

We explicitly construct a double-field inflationary model, which satisfies the latest Planck constraints at the cosmic microwave background (CMB) scales and produces the whole dark matter energy density as primordial black holes (PBHs), in the mass range ${10}^{\ensuremath{-}17}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}\ensuremath{\lesssim}{M}_{\mathrm{PBH}}\ensuremath{\lesssim}{10}^{\ensuremath{-}13}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. The PBHs can be produced after the end of slow-roll inflation from the bubbles of true vacuum that nucleate during the course of inflation. Obtaining PBHs in this mass range enforces the scale of inflation to be extremely low, ${10}^{\ensuremath{-}7}\ensuremath{\lesssim}H\ensuremath{\lesssim}{10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{GeV}$, which makes the efforts to observe gravitational waves at the CMB scales futile, although it is high enough to allow for a successful big bang nucleosynthesis. We will show that the shape of the mass distribution of the PBHs is dependent on how inflation ends and the Universe settles from the metastable direction to the true one. End of inflation can also be probed by examining the gravitational waves spectrum. In particular, we show that if exit from the rolling metastable direction to the true vacuum of the potential happens through a first-order phase transition after the end of slow-roll inflation, it leaves behind a stochastic gravitational wave background (SGWB), which is potentially observable by the Laser Interferometer Space Antenna. Examining the mass distribution of PBHs and possible SGWB from the end of inflation, we may be able to gain invaluable information about the end of inflation.