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The detection of a primordial stochastic gravitational wave background hasthe potential to reveal unprecedented insights into the early universe, andpossibly into the dynamics of inflation. Generically, UV-complete inflationarymodels predict an abundance of light scalars, so any inflationary stochasticbackground may well be formed in a model with several interacting degrees offreedom. The stochastic backgrounds possible from two-field inflation have beenwell-studied in the literature, but it is unclear how similar they are to thepossibilities from many-field inflation. In this work, we study stochasticbackgrounds from more-than-two field inflation for the first time, focusing onthe scalar-induced background produced by a brief turn in three-field space. Wefind an analytic expression for the enhancement in the power spectrum as afunction of the turn rate and the torsion, and show that unique signatures ofthree-field dynamics are possible in the primordial power spectrum andgravitational wave spectrum. We confirm our analytic results with a suite ofnumerical simulations and find good agreement in the shape and amplitude of thepower spectra. We also comment on the detection prospects in LISA and otherfuture detectors. We do not expect the moderately large growth of theinflationary perturbations necessary for detection to cause a breakdown ofperturbation theory, but this must be verified on a case-by-case basis forspecific microphysical models to make a definitive claim.

Primordial Stochastic Gravitational Wave Backgrounds from a Sharp Feature in Three-field Inflation