Gravitational Waves from Primordial Black Holes formed by Null Energy Condition Violation during Inflation

Abstract

A transient violation of the null energy condition (NEC) during inflation provides a novel mechanism for producing primordial black holes (PBHs) and stochastic gravitational wave (GW) backgrounds. In this work, we extend previous studies by computing the GW contributions from both the ringdown phase of PBH formation and subsequent binary mergers. Our results show that this scenario produces a rich, multi-component GW spectrum consisting of primordial GWs, scalar-induced GWs, and GW emissions from PBH ringdown and binary mergers. We demonstrate that these correlated signatures across different frequency bands provide a novel and powerful avenue to probe or constrain NEC violation during inflation through future multi-band GW observations.

Figures (2)

• Figure 1: Schematic illustration of the GW generation framework driven by an intermediate NEC violation during inflation. The inflationary NEC-violating stage is characterized by an increasing Hubble parameter (i.e., $\dot{H}>0$), which triggers an enhancement of the primordial power spectra $P_\zeta$ and $P_T$. This mechanism leads to three key predictions: PGWs, SIGWs and PBHs. PBHs further contribute to the GW background through two key channels: the initial ringdown during their formation and later-stage binary mergers.
• Figure 2: Predicted energy spectra of the stochastic GW background for four different parameter sets (distinguished by color). These curves correspond to those of the same colors in Figs. 3 to 5 of Ref. Cai:2023uhc, namely, curves of the same color share identical parameter settings. The various line styles denote different generation mechanisms: thick solid curves for SIGWs; dotted curves for PGWs; dashed curves for the QNM radiation during the ringdown phase of newly formed PBHs; and thin solid curves for the binary PBH mergers. Here, the results for SIGWs and PGWs are adopted from Fig. 5 of Ref. Cai:2023uhc. The shaded regions and boundary curves represent sensitivities of current and future GW observatories, including PTAs (EPTA, NANOGrav, SKA), space-based detectors (THEIA, $\mu$ARES, LISA, Taiji, TianQin, BBO, DECIGO), and ground-based interferometers (LIGO, ET, CE), see e.g. Roshan:2024qnv and references therein.