Production of Gravitational Waves from Preheating and Tachyonic Instabilities

We analyze GW production during preheating for an $\alpha$-attractor potential terminating in the positive-curvature regime, with energy transfer via $\phi {\chi }^2$. Linear Floquet analysis and nonlinear simulations show that $\phi$ fluctuations grow by parametric resonance, while $\chi$ undergoes tachyonic bursts. The GW spectrum features two peaks: a dominant low-frequency peak from the parametric channel and a subdominant high-frequency peak from the tachyonic channel. Redshifted to today, the peak reaches $h^2{\mathrm{\Omega }}_{\mathrm{G}\mathrm{W}}^{(0)}\sim {10}^{-11}$ at $f_p^{(0)}\sim {10}^7$ Hz. This multi-peak structure is a characteristic imprint of trilinear preheating in $\alpha$-attractors.