We identify a characteristic pattern in the scalar-induced stochastic gravitational wave background from particle production during inflation. If particle production is sufficiently efficient, the scalar power spectrum exhibits O(1) oscillations periodic in k, characteristic of a sharp feature, with an exponentially enhanced envelope. We systematically study the properties of the induced spectrum of gravitational waves sourced after inflation and find that this inherits the periodic structure in k, resulting in a peak in the gravitational wave energy density spectrum with O(10%) modulations. The frequency of the oscillation in the scalar power spectrum is determined by the scale of the feature during inflation and in turn sets the frequency of modulations in the gravitational wave signal. We present an explicit realisation of this phenomenon in the framework of multifield inflation, in the form of a strong sharp turn in the inflationary trajectory. The resulting stochastic background is potentially detectable in future gravitational wave observatories, and considerations of backreaction and perturbativity can be used to constrain the parameter space from the theoretical side. Our work motivates more extensive research linking primordial features to observable properties of the stochastic background of gravitational waves, and dedicated development in data analysis for their detection.

Several recent proposals to embed inflation into high-energy physics rely on inflationary dynamics characterized by a strongly non-geodesic motion in negatively curved field space. This naturally leads to a transient instability of perturbations on sub-Hubble scales, and to their exponential amplification. Supported by first-principle numerical computations, and by the analytical insight provided by the effective field theory of inflation, we show that the bispectrum is enhanced in flattened configurations, and we argue that an analogous result holds for all higher-order correlation functions. These "hyper non-Gaussianities" thus provide powerful model-independent constraints on non-standard inflationary attractors motivated by the search for ultraviolet completions of inflation.Introduction.-Negatively curved field space plays a crucial role in modern embeddings of inflation in highenergy physics. Non-linear sigma models with a hyperbolic target space arise naturally in top-down realizations of inflation, particularly within supergravity, giving rise to the α-attractor class of models (see e.g. [1][2][3]). Independently of the question of their ultraviolet completions, non-minimal kinetic terms of the hyperbolic type lead to interesting dynamics, allowing for non-trivial inflationary trajectories characterized by a strongly non-geodesic motion [4][5][6][7]. This in turn relaxes the conditions of slow-roll to allow for potentials that are steep in Planck units [8,9], a welcome feature in view of the eta problem and the recently much discussed swampland conjectures [10,11]. Lastly, internal field spaces with negative curvature are at the origin of the phenomenon of geometrical destabilization [12][13][14][15][16], in which non-inflationary degrees of freedom, even heavy ones, can dramatically affect the fate of inflation.A concrete scenario in which the consequences of a hyperbolic field space have been studied is the proposal of "hyperinflation" [17], that has recently been under scrutiny [18,19]. The intuitive picture of this set-up is that of an inflationary trajectory corresponding to a circular motion around the minimum of a (circularly symmetric) scalar potential. The hyperbolic geometry is crucial to compensate for the loss of angular velocity to the Hubble friction, allowing inflation to last long enough, even if the potential is too steep to inflate along a radial trajectory. Within this circumstance, hyperinflation proceeds along a strongly non-geodesic trajectory, and a striking outcome is an exponential growth of the curvature power spectrum around the time of Hubble crossing, and the corresponding suppression of the tensor-toscalar ratio. With such an amplification, assessing the size of nonlinear effects in this setup appears to be crucial, while previous studies have restricted their attention to the analysis of linear fluctuations.In this context, this Letter presents a general framework to study non-Gaussianities in the presence of strongly non-geodesic motion typical of hyperbolic-type geometry, ...