Lattice simulations of scalar-induced gravitational waves from inflation

Abstract

Scalar-induced gravitational waves (SIGWs) provide a powerful probe of inflationary dynamics on scales far smaller than those accessible to the cosmic microwave background and large-scale structure. In scenarios with a transient ultra-slow-roll (USR) phase, the curvature power spectrum can be strongly enhanced on small scales, potentially generating an observable stochastic GW background. In this regime, scalar dynamics during inflation can become nonlinear, challenging the validity of standard perturbative predictions. Existing semi-analytical calculations of SIGWs rely on the linear evolution of inflation fluctuations. In this work, we compute SIGWs from USR inflation using lattice simulations. We evolve the inflaton field fully nonlinearly during inflation and extract the curvature perturbation nonperturbatively, then simulate its post-reheating horizon re-entry by evolving the Newtonian potential linearly while retaining the full non-Gaussian structure of the initial conditions for the primordial fluctuations in the tensor source. For moderate non-Gaussianity, the semi-analytical prediction captures the correct order of magnitude of the GW signal but receives important corrections. When inflationary non-Gaussianities are large, it can fail dramatically in both amplitude and spectral shape, independently of the overall size of the tensor power spectrum. Our results show that reliable predictions of SIGWs in such scenarios require nonperturbative control of the inflationary scalar dynamics. The code used for this work is available at https://github.com/caravangelo/inflation-easy.git.

Figures (9)

• Figure 1: Simulation pipeline: From sub-horizon inflaton fluctuations (a), we obtain the super-horizon curvature perturbation (b) using the lattice simulation of inflation. This curvature field is then mapped to the super-horizon Newtonian potential after inflation (c), which sets the initial conditions for the simulation of horizon re-entry. Evolving this system yields the sub-horizon Newtonian potential (d). The total gravitational-wave signal contains two contributions: the inflationary component (GW 1), emitted at horizon exit, and the post-reheating component generated at horizon re-entry (GW 2). The GWs would then travel freely to reach late time observers, like LISA, shown as an example. Figure adapted from Caravano:2025klk.
• Figure 2: Top: Lattice curvature power spectra from Caravano:2025diq, compared with linear perturbation theory. Middle: Scalar-induced GW spectra for the same models. Bottom: Fractional residuals with respect to the (semi-)analytical standard calculation. In all panels, different colours correspond to different values of the peak tree-level power spectrum, as indicated in the legend. Solid curves with circular markers show the full lattice result, dashed curves show the standard semi-analytical prediction using the linear power spectrum, and dotted curves show the semi-analytical calculation using the lattice-derived curvature spectra from the top panel.
• Figure 3: Top: Evolution of the spatially averaged inflaton velocity in the large NG case, compared with the prediction obtained from the background Klein--Gordon equation. Bottom: Inflaton power spectrum at the final simulation time compared with the linear prediction of the Mukhanov--Sasaki equation. Colors correspond to the legend in Fig. \ref{['fig:mild']}.
• Figure 4: Same as Fig. \ref{['fig:mild']}, but for the models with large non-Gaussianity presented in Sec. \ref{['large-NG']}.
• Figure 5: Top: One-point PDF of the inflaton field at different simulation times in the large-NG cases, as indicated by the colorbar in the top-left panel. Bottom: Final time PDF of $\zeta$, computed using both the linear relation between $\delta\phi$ and $\zeta$ and the fully nonperturbative $\delta N$ extraction (see Caravano:2025diqCaravano:2025klk for details on the lattice procedure). Different columns correspond to different values of the peak tree-level curvature power spectrum.