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We study the tachyonic resonance preheating generated from the bosonic trilinear $\phi\chi^2$ interactions following inflation period caused by the quartic inflationary potential $\lambda\phi^4/4$. In particular, we focus on the effects of expansion of the Universe during the preheating era. The trilinear interaction, in contrast to the four-leg $\phi^2\chi^2$,
breaks the conformal symmetry explicitly and the resonant source term becomes non-periodic, making the Floquet theorem inapplicable. We find that the occupation number of the produced $\chi$-particles has a non-linear exponential growth with exponent $\sim x^{3/2}$, where $x$ is the conformal time.
This should be contrasted with preheating from a periodic resonant source, arising for example from four-legs $\phi^2\chi^2$ interaction, where the occupation number has a linear exponential growth. We present an analytic method to compute the interference term coming from phases accumulated in non-tachyonic scattering regions and show that the effects of
the interference term causes ripples on $x^{3/2}$ curve, a result which is
confirmed by numerical analysis. Studying the effects of back-reaction of the $\chi$-particles, we show that tachyonic resonance preheating in our model can last long enough to transfer most of the energy from the background inflation field $\phi$, providing an efficient model for preheating in the chaotic inflation models.
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