Matrix inflation, or M-flation, is a string theory motivated inflationary model with three scalar field matrices and gauge fields in the adjoint representation of the $\mathbf{U}(N)$ gauge group. One of these $3N^2$ scalars appears as the effective inflaton while the rest of the fields (scalar and gauge fields) can play the role of isocurvature fields during inflation and preheat fields afterwards. There is a region in parameter space and initial field values, "the hilltop region," where predictions of the model are quite compatible with the recent \textit{Planck} data.
We show that in this hilltop region, if the inflaton ends up in the supersymmetric vacuum, the model can have an embedded preheating mechanism.
% only if inflation happens around the supersymmetric vacuum. %
Couplings of the preheat modes are related to the inflaton self-couplings and therefore are known from the CMB data. Through lattice simulations performed
using a symplectic integrator, we numerically compute the power spectra
of gravitational waves produced during the preheating stage following M-flation. The preliminary numerical simulation of the spectrum from multi-preheat fields peaks in the GHz band with an amplitude $\Omega_{\mathrm{gw}}h^{2} \propto 10^{-16}$, suggesting that the model has concrete predictions for the ultra-high frequency gravity-wave probes. This signature could be used to distinguish the model from rival inflationary models.