Bispectrum of induced gravitational waves in the poltergeist mechanism

TL;DR

This paper computes the tensor bispectrum of gravitational waves generated by the poltergeist mechanism, where an extended early matter-dominated era is followed by a rapid transition to radiation domination at $\eta_R$. Using the sudden-transition approximation, it derives a time-integrated kernel and separates contributions from the MD and RD epochs to the tensor bispectrum, highlighting a unique scale-dependent shift between equilateral and squeezed configurations. A key result is the existence of a critical perimeter $\mathcal{C}_c \approx 1.05\,k_{\max}$ that governs whether the bispectrum’s global maximum lies in the squeezed or equilateral shape, providing a distinctive signature of the poltergeist transition. These findings offer observable diagnostics for future GW detectors and help distinguish poltergeist-induced non-Gaussianity from other generation mechanisms.

Abstract

In the poltergeist mechanism the enhancement of induced gravitational waves (GWs) occurs due to a sudden transition from an early matter-dominated era to the radiation-dominated era. In this work, we calculate the bispectrum of induced GWs from the poltergeist mechanism by adopting the sudden transition approximation. We find that the tensor bispectrum peaks either in the equilateral or squeezed configurations, depending on scales. Such a characteristic behavior enables us to distinguish it from that from other GW generation mechanisms.

Figures (4)

• Figure 1: Bispectrum of gravitational waves in the matter-radiation transition model for the equilateral shape. We plot the dimensionless bispectra for two independent polarization modes (RRR, RRL) in the equilateral shape, represented by the red solid line and gray dashed line in the figure, respectively.
• Figure 2: Schematic of the bispectrum for the RRR polarization mode in the squeezed shape. Considering the requirement for the lower limit of the wavenumber $k$, the left boundary of the abscissa is set to $1/225$.
• Figure 3: The bispectrum with different $\mathcal{C}$, where $C_{\rm c}=1.05k_{\max}$. The positions of the equilateral shape on the bispectrum curve is represented by the dots in the figure. The left boundary is set to $k=k_{\max}/225$, which corresponds to the squeezed shape.
• Figure 4: The dependence of the bispectrum on the perimeter $\mathcal{C}$. The purple dots represent the intersection points of the two curves, corresponding to the case where the bispectrum of the squeezed shape equals that of the equilateral shape.