Some exact results in preheating from the Lamé equation

Abstract

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 shown to be of the form V(ф) = λ ф ^(4) /4 + K ф^( )2 /2 + μ/(2 ф^( 2) ) + V_(0). As an application, we study the preheating phase after inflation with K = 0 and arbitrary λ, μ > 0. For certain values of the coupling constant between the inflaton and the matter fields, we show how the instability intervals, the characteristic exponents, and the particle production can be computed in closed form.