We study gravitational waves (GWs) induced by non-Gaussian curvature perturbations. We calculate the density parameter per logarithmic frequency interval, ${\mathrm{\Omega }}_{\mathrm{GW}}(k)$, given that the power spectrum of the curvature perturbation ${\mathcal{P}}_{\mathcal{R}}(k)$ has a narrow peak at some small scale $k_{*}$, with a local-type non-Gaussianity, and constrain the nonlinear parameter $f_{\mathrm{NL}}$ with the future LISA sensitivity curve as well as with constraints from the abundance of the primordial black holes (PBHs). We find that the non-Gaussian contribution to ${\mathrm{\Omega }}_{\mathrm{GW}}$ increases as $k^3$, peaks at $k/k_{*}=4/\sqrt{3}$, and has a sharp cutoff at $k=4k_{*}$. The non-Gaussian part can exceed the Gaussian part if ${\mathcal{P}}_{\mathcal{R}}(k)f_{\mathrm{NL}}^2\gtrsim 1$. If both a slope ${\mathrm{\Omega }}_{\mathrm{GW}}(k)\propto k^{\beta }$ with $\beta \sim 3$ and the multiple-peak structure around a cutoff are observed, it can be recognized as a smoking gun of the primordial non-Gaussianity. We also find that if PBHs with masses of $10^{20}$ to $10^{22}\mathrm{g}$ are identified as cold dark matter of the Universe, the corresponding GWs must be detectable by LISA-like detectors, irrespective of the value of ${\mathcal{P}}_{\mathcal{R}}$ or $f_{\mathrm{NL}}$.

We study the general infrared behavior of the power spectrum of a stochastic gravitational wave background produced by stress tensor in the form bilinear in certain dynamical degrees of freedom. We find ${\mathrm{\Omega }}_{\mathrm{GW}}\propto k^3$ for a very wide class of the sources which satisfy a set of reasonable conditions. Namely, the $k^3$ scaling is universally valid when the source term is bounded in both frequency and time, is effective in a radiation-dominated stage, and for $k$ smaller than all the physical scales associated with the source, like the peak frequency, peak width, and time duration, etc. We also discuss possible violations of these conditions and their physical implications.

We present a new realization of the resonant production of primordial black holes as well as gravitational waves in a two-stage inflation model consisting of a scalar field $\varphi$ with an axion-monodromy-like periodic structure in the potential that governs the first stage and another field $\chi$ with a hilltoplike potential that dominates the second stage. The parametric resonance seeded by the periodic structure at the first stage amplifies the perturbations of both fields inside the Hubble radius. While the evolution of the background trajectory experiences a turn as the oscillatory barrier height increases, the amplified perturbations of $\chi$ remain as they are and contribute to the final curvature perturbation. It turns out that the primordial power spectrum displays a significant resonant peak on small scales, which can lead to an abundant production of primordial black holes. Furthermore, gravitational waves are also generated from the resonantly enhanced field perturbations during inflation, the amplitude of which may be constrained by future gravitational wave interferometers.