Comprehensive analysis of dissipative effects in the induced gravitational waves

TL;DR

This work develops a comprehensive framework for dissipative effects in gravitational waves induced by curvature perturbations, showing that fluid viscosity and diffusion imprint distinctive features on the IGW spectrum, especially near the horizon scale at decoupling $k_{ ext{H,dec}}$. Through a detailed treatment of a damping scale $k_D$ and the evolution of scalar perturbations, the authors demonstrate robust phenomenology across scale-invariant, monochromatic, and log-normal curvature spectra, including a characteristic double-valley suppression and infrared modifications governed by dissipation parameters $\\alpha$ and $\\gamma$. They connect these features to observable signals in pulsar timing arrays and future GW experiments, arguing that neutrino decoupling in the Standard Model and possible new weakly interacting particles could be probed via dissipation-induced signatures, with implications for high-energy physics scales $M_{W'}$. The paper further extends the analysis to primordial non-Gaussianity, IGW anisotropies, and the poltergeist mechanism, highlighting how dissipation interacts with these extensions and offering a unified pathway to constrain early-Universe physics through gravitational waves. Overall, dissipative effects provide a more realistic template for IGWs and open a new avenue to explore fundamental physics at extremely high energies using upcoming GW observations.

Abstract

Dissipation is an intrinsic property of the cosmic fluid, leading to the damping of curvature perturbations at small scales. In this paper, we comprehensively study dissipative effects in gravitational waves induced by curvature perturbations, known as induced gravitational waves (IGWs). We find dissipative effects become especially significant at wavenumber $k \sim k_{\mathcal{H},\mathrm{dec}}$, where $k_{\mathcal{H},\mathrm{dec}}$ corresponds to the horizon scale at the decoupling of weakly-interacting particles. They can leave characteristic features on the IGW spectrum, including a notable suppression with a ``double-valley'' structure at $k \sim k_{\mathcal{H},\mathrm{dec}}$ and a modified infrared behavior without logarithmic running at $k \lesssim k_{\mathcal{H},\mathrm{dec}}$. Within the Standard Model of particle physics, dissipative effects caused by neutrinos at the nanohertz frequencies can be important in the analysis of pulsar timing array data. Furthermore, dissipation-induced features associated with possible new weakly-interacting particles can be detectable by a wide range of gravitational-wave experiments, serving as a promising probe of new physics at extremely high energy scales. As an extension, we also discuss dissipative effects in the presence of primordial non-Gaussianity and their impacts on the anisotropies of IGWs and the poltergeist mechanism. These dissipative effects not only provide a more realistic description of IGWs but also exhibit rich phenomenology and profound physical implications, opening a new window into understanding the early Universe and fundamental physics.

Figures (14)

• Figure 1: Temperature dependence of the damping scale $k_{D}$. Red solid line stands for the SM Jeong:2014gna, while red dashed lines denote BSM. We plot the comoving Hubble horizon $k_\mathcal{H}=aH$ for comparison.
• Figure 2: Damping scale $\kappa_D$ as a function of $\hat{\tau}$ near the particle decoupling for different values of $\alpha$ and $\gamma$. The comoving Hubble parameter $\kappa_\mathcal{H}=1/\hat{\tau}$ is also plotted.
• Figure 3: Energy-density spectrum $\Omega_\mathrm{gw}$ (normalized by $\Omega_\mathrm{gw}^{\kappa_D\rightarrow \infty}=0.822\,\mathcal{A}_\zeta^2$) versus the scale $\kappa$ for scale-invariant primordial curvature power spectra. In the left panel, we fix $\alpha=5$ and take $\gamma=0.05, 0.1, 0.2, 0.4, 0.8$. In the right panel, we fix $\gamma=0.3$ and take $\alpha=3,4,5,6,7$.
• Figure 4: The 3D graph and heat map of $\omega_\mathrm{gw}^{\kappa_D\rightarrow\infty}(1,1,\kappa,\hat{\tau}_1,\hat{\tau}_2)$ as a function of $\kappa\hat{\tau}_1$ and $\kappa\hat{\tau}_2$. The red and blue regions correspond to the positive and negative values, respectively. In the right panel, we mark the integral regions given by the "dissipation-induced lifetimes" of the modes $\kappa_a=2$ (blue dashed lines), $\kappa_b=6$ (green dashed lines), and $\kappa_c=18$ (red dashed lines).
• Figure 5: Left panel: Energy-density spectrum $\Omega_\mathrm{gw}$ (normalized by $\Omega_\mathrm{gw}^{\kappa_D\rightarrow \infty}=0.822\,\mathcal{A}_\zeta^2$) versus the scale $\kappa$ for scale-invariant primordial curvature power spectra. Right panel: Damping scale $\kappa_D$ as a function of $\hat{\tau}$ near the particle decoupling. In both panels, we mark the several reference scales (i.e., $\kappa_a=2$, $\kappa_b=6$, and $\kappa_c=18$), which correspond to the positions of peaks/valleys in $\Omega_\mathrm{gw}$. We set $\alpha=5$ and $\gamma=0.3$.