Gravitational Wave Production right after a Primordial Black Hole Evaporation (2003.10455v3)

Abstract: We discuss the footprint of evaporation of primordial black holes (PBHs) on stochastic gravitational waves (GWs) induced by scalar perturbations. We consider the case where PBHs once dominated the Universe but eventually evaporated before the big bang nucleosynthesis. The reheating through the PBH evaporation could end with a sudden change in the equation of state of the Universe compared to the conventional reheating caused by particle decay. We show that this "sudden reheating" by the PBH evaporation enhances the induced GWs, whose amount depends on the length of the PBH-dominated era and the width of the PBH mass function. We explore the possibility to constrain the primordial abundance of the evaporating PBHs by observing the induced GWs. We find that the abundance parameter $\beta \gtrsim 10^{-5} \text{ - }10^{-8}$ for $\mathcal{O}(10^3 \text{ - } 10^5) \, \text{g}$ PBHs can be constrained by future GW observations if the width of the mass function is smaller than about a hundredth of the mass.

Gravitational Wave Production Following Primordial Black Hole Evaporation

This paper presents a comprehensive paper of gravitational wave (GW) generation following the evaporation of primordial black holes (PBHs) in the early universe. The authors address the implications of PBH evaporation for stochastic GWs induced by scalar perturbations. Specifically, the work explores scenarios where PBHs initially dominated the universe, subsequently evaporating before the onset of big bang nucleosynthesis. The PBH domination gives rise to what the authors describe as a "sudden reheating" event, significantly affecting the subsequent evolution and GW production.

Our Approach and Numerical Analysis

The investigation focuses on the scenario in which PBHs dominate the universe's energy density, transitioning abruptly to a radiation-dominated era via Hawking evaporation. This transition involves a rapid change in the equation of state due to the PBHs' mass variance and decay rate characteristics. The extent of GW enhancement depends on the duration of PBH domination, primarily determined by PBH mass and initial abundance, and the width of the mass spectrum.

The authors employ analytic and numerical techniques to estimate the magnitude of GWs induced by these transitions. They detail the interaction of scalar perturbations under varying PBH mass distributions, employing a mix of synchronous and Newtonian gauge calculations to elucidate fluctuations' behavior and demonstrate numerical results showing how PBH evaporation leads to notable GW amplitude fluctuations.

Key Results and Observations

The paper predicts a considerable spectrum of induced GWs observable by upcoming detectors such as DECIGO, BBO, and LISA if certain mass function conditions are met. For precise calculations, the authors propose that GWs can be substantially enhanced by the so-called Poltergeist mechanism, where fast oscillations occur in the gravitational potential at the radiation transition—a phenomenon requiring a narrow PBH mass function for observability due to its sudden nature.

They derive constraints on the initial abundance parameter $\beta$, speculating that if the width of the mass function is sufficiently narrow (less than about 0.01), the GWs can be potentially detected in future observations. The research suggests that PBH evaporation results in strong GW signals if the duration of the PBH-dominated phase is substantial, allowing for constraints on the primordial abundance of evaporating PBHs.

Theoretical and Practical Implications

The paper strengthens theoretical understanding of early universe processes where PBHs form and evaporate, providing a mechanism for probing scalar perturbations inaccessible via conventional cosmic microwave background methods.

The authors emphasize the potential for detecting GWs induced by the Poltergeist mechanism as a means of constraining PBH populations, thus adding a new dimension to our understanding of PBH-driven cosmology. There are notable practical implications, particularly for dark matter models. The evaporation process compared to massive dark matter genesis underscores the significance of PBHs for cosmological models including baryogenesis.

Conclusion

This research contributes profoundly to the exploration of PBH role in cosmology. It provides a framework for the future hunt and detection of elusive tiny PBHs via GW observations. Researchers can now speculate on broader implications for models of cosmic evolution, inflationary scenarios, and dark matter genesis in relation to PBH evaporation events, marking an advancement in particle cosmology and gravitational wave astrophysics.