Third-order scalar induced gravitational waves during a matter-dominated era: secular growth and implications for primordial black hole domination

@misc{zhou2026thirdorder,
  title = {{Third-order scalar induced gravitational waves during a matter-dominated era: secular growth and implications for primordial black hole domination}},
  author = {Jing-Zhi Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08045},
  eprint = {2610.08045},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08045},
}

TY  - UNPB
TI  - Third-order scalar induced gravitational waves during a matter-dominated era: secular growth and implications for primordial black hole domination
AU  - Jing-Zhi Zhou
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08045
UR  - https://arxiv.org/abs/2610.08045
AB  - We investigate scalar induced gravitational waves (SIGWs) at third-order during a matter-dominated (MD) era. We classify the sources into four parts---built from three first-order scalars, and from a first-order scalar times the second-order tensor, vector, and scalar perturbations---and obtain all four kernel functions analytically in closed form. Unlike their radiation-dominated counterparts, the MD kernel functions grow secularly, translating into a rapid growth of the spectrum, Ω^(3)_GW∝ x^6 versus Ω^(2)_GW∝ x^2 at x≡ kη≫1. We derive the third-order power spectrum as a five-fold integral for a general primordial spectrum, and evaluate it numerically for a monochromatic one, where all contributions from the second-order vector source vanish identically. As an application, we consider the early MD era driven by primordial black holes (PBHs) before their evaporation. Requiring that the induced gravitational waves do not backreact on the cosmological perturbations, ∫dln k Ω^tot_GW<1 then bounds the initial PBH abundance as Ω_PBH,f≲4.6×10^−7 (m_PBH/10^7 g)^−0.48, about three orders of magnitude stronger than the second-order-only bound. Our results indicate that higher-order SIGWs inevitably become nonperturbative during a sufficiently long MD era, with important implications for scenarios involving an early matter domination.
ER  -