The poltergeist mechanism -- Enhancement of scalar-induced gravitational waves with early matter-dominated era

TL;DR

The paper investigates scalar-induced gravitational waves (SIGWs) generated by primordial density perturbations as a probe of the early Universe's thermal history, focusing on an early matter-dominated (eMD) era and its sudden transition to a pressure-dominated era (e.g., radiation or kination). It explains the poltergeist mechanism, where a rapid eMD→RD transition causes subhorizon density perturbations to oscillate with large amplitude, dramatically boosting SIGWs beyond their standard radiation-era levels. The authors develop the background and perturbation framework for MD/RD transitions, derive the SIGW spectrum using Green's-function methods, and distinguish gradual versus sudden transitions with concrete examples including PBH evaporation, Q-balls/oscillons, and axion rotation scenarios. They highlight observational prospects for LISA/DECIGO/BBO and PTA experiments, and discuss limitations from nonlinearities and diffusion that must be addressed to robustly connect SIGWs to early-Universe physics. Overall, the work provides a comprehensive treatment of the poltergeist mechanism as a novel probe of nonstandard cosmological epochs and their particle-physics realizations.

Abstract

Gravitational waves induced by primordial density perturbations provide a powerful probe of the Universe's thermal history, which may include an early matter-dominated (eMD) era predicted by well-motivated particle-physics models. The induced GWs can be significantly enhanced when the Universe undergoes a sudden transition from an eMD era to an era with pressure, such as a radiation or kination era. This enhancement arises from the growth of density perturbations during the eMD era and their rapid oscillations during the era with pressure. This phenomenon is called the poltergeist mechanism. In this review, we explain the essence of the poltergeist mechanism and explore concrete scenarios in which such an enhancement can occur.

Figures (19)

• Figure 1: The evolution of the background quantities and the fitting functions, given by Eqs. (\ref{['eq:a_app']}) and (\ref{['eq:w_fit']}). From Inomata:2019zqy.
• Figure 2: The evolution of the perturbations. $\Phi_{\text{fit}}$ is given by Eq. \ref{['eq:phi_app_f']}. From Inomata:2019zqy.
• Figure 3: The comparison between the numerical results of $\Phi$ and the fitting function, given by Eq. (\ref{['eq:phi_app_f']}). From Inomata:2019zqy.
• Figure 4: The GW spectrum at $\eta_\text{c}$ in the case of the gradual transition. The primordial curvature power spectrum is given by Eq. (\ref{['eq:pzeta']}) with $k_\text{max}= 450/\eta_\text{R}$ for all the plots. The black line for $\Omega_\text{GW}$ is the sum of $\Omega_{\text{GW,eMD}}$, $\Omega_{\text{GW,RD}}$, and $\Omega_{\text{GW,cross}}$. For comparison, we show the GW spectrum (brown dotted line) with the implicit assumption that the previous work Assadullahi:2009nf makes: $\Phi=1$ until $\eta = \eta_\text{R}$ and there is no GW production for $\eta > \eta_\text{R}$ ($I_\text{RD} =0$). From Inomata:2019zqy.
• Figure 5: Analogy to a pendulum in a medium with time-dependent friction. The pendulum with a fixed length corresponds to a mode of $\Phi$ with a fixed comoving wavenumber $k$. The deeper/lighter bluish background color indicates the stronger/weaker friction in analogy to the (conformal) Hubble friction, respectively. \ref{['sfig:damped_osc']} The oscillation amplitude is damped by the (time-dependent) friction in analogy to the usual behavior of the gravitational potential, e.g., in a RD era. The yellow arrow schematically shows the damping of the oscillations. The amplitude has been damped since the horizon reentry of the mode. The induced GWs are not enhanced in this case. \ref{['sfig:fixed_osc']} The position of the oscillator is kept fixed while the friction of the medium is large, so the amplitude is not damped. This is analogous to the behavior of the gravitational potential in a MD era. \ref{['sfig:released_osc']} When "poltergeist's hand" abruptly releases the oscillator, it begins to oscillate. By this time, the friction of the medium becomes weak. This is analogous to the behavior of the gravitational potential after a sudden transition from the eMD era to the RD era. The rapid oscillation with respect to the Hubble parameter with the undamped amplitude efficiently produces the GWs.