Gravitational waves from a universe filled with primordial black holes

Ultra-light primordial black holes, with masses m(PBH) < 10(9)g, evaporate before big-bang nucleosynthesis and can therefore not be directly constrained. They can however be so abundant that they dominate the universe content for a transient period (before reheating the universe via Hawking evaporation). If this happens, they support large cosmological fluctuations at small scales, which in turn induce the production of gravitational waves through second-order effects. Contrary to the primordial black holes, those gravitational waves survive after evaporation, and can therefore be used to constrain such scenarios. In this work, we show that for induced gravitational waves not to lead to a backreaction problem, the relative abundance of black holes at formation, denoted Omega(PBH,f), should be such that Omega(PBH,f) < 10(-4)(m(PBH)/10(9)g)(-1/4). In particular, scenarios where primordial black holes dominate right upon their formation time are all excluded (given that m(PBH) > 10 g for inflation to proceed at rho(1/4) < 10(16)GeV). This sets the first constraints on ultra-light primordial black holes.

Automated summary

Ultra-light primordial black holes, with masses less than 10(9)g, can dominate the universe for a transient period and induce cosmological fluctuations and gravitational waves. To avoid backreaction problems with induced gravitational waves, there are constraints on the relative abundance of black holes at formation.