Publication: The Lame equation in parametric resonance after inflation
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2000-10-17
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American Physical Society
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Abstract
We show that the most general inflaton potential in Minkowski spacetime for which the differential equation for the Fourier modes of the matter fields reduces to Lame's equation is of the form V(phi)=lambda phi^4/4+Kphi^2/2+mu/(2 phi^2)+V_0. As an application, we study the preheating phase after inflation for the above potential with K=0 and arbitrary lambda,mu >0. For certain values of the coupling constant between the inflaton and the matter fields, we calculate the instability intervals and the characteristic exponents in closed form.
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© 2000 The American Physical Society. A.L.M. wishes to thank J. García-Bellido for useful discussions. This work was partially supported by grants DGES PB98-0821 and DGICYT AEN97-1693.
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[16] If the x field had a mass m_x , the only change in the above derivation would be to replace k^2 in Eqs. (8) and (12) by k^2 + m^2_x. These changes have no effect on Eq. (15).
[17] See also the forthcoming paper by J. García-Bellido for an extension of this method.