  The detection of a primordial stochastic gravitational wave background has
the potential to reveal unprecedented insights into the early universe, and
possibly into the dynamics of inflation. Generically, UV-complete inflationary
models predict an abundance of light scalars, so any inflationary stochastic
background may well be formed in a model with several interacting degrees of
freedom. The stochastic backgrounds possible from two-field inflation have been
well-studied in the literature, but it is unclear how similar they are to the
possibilities from many-field inflation. In this work we study stochastic
backgrounds from more-than-two field inflation for the first time, focusing on
the scalar-induced background produced during the radiation era by a brief turn
in three-field space. We find an analytic expression for the enhancement in the
power spectrum as a function of the turn rate and the torsion, and show that
unique signatures of three-field dynamics are possible in the primordial power
spectrum and gravitational wave spectrum. We confirm our analytic results with
a suite of numerical simulations and find good agreement in the shape and
amplitude of the power spectra. We also comment on the detection prospects in
LISA and other future detectors. We do not expect the moderately large growth
of the inflationary perturbations necessary for detection to cause a breakdown
of perturbation theory, but this must be verified on a case-by-case basis for
specific microphysical models to make a definitive claim.
