Tachyonic Resonance Preheating in Expanding Universe

In this paper the tachyonic resonance preheating generated from the bosonic trilinear $\phi\chi^2$ interactions in an expanding Universe is studied. In $\lambda\phi^4/4$ inflationary model the trilinear interaction, in contrast to the four-legs $\phi^2\chi^2$, 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 the 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.