STRUCTURE OF RESONANCE IN PREHEATING AFTER INFLATION

We consider preheating in the theory 1/4 lambda phi(4)+1/2g(2) phi(2) chi(2), where the classical oscillating inflaton field phi(t) decays i nto chi particles and phi particles. The parametric resonance which le ads to particle production in this conformally invariant theory is des cribed by the Lame equation. It significantly differs from the resonan ce in the theory with a quadratic potential. The structure of the reso nance depends in a rather nontrivial way on the parameter g(2)/lambda. We find an ''unnatural selection'' rule: the most efficient creation of particles occurs not for particles which have the strongest couplin g to the inflaton field, but for those which have the greatest charact eristic exponent mu. We construct the stability-instability chart in t his theory for arbitrary g(2)/lambda. We give simple analytic solution s describing the resonance in the limiting cases g(2)/lambda much less than 1 and g(2)/lambda much greater than 1, and in the theory with g( 2)=3 lambda, and with g(2)=lambda. From the point of view of parametri c resonance for chi, the theories with g(2)=3 lambda and with g(2)=lam bda have the same structure, respectively, as the theory 1/4 lambda ph i(4), and the theory (lambda/4N)(phi(i)(2))(2) of an N-component scala r field phi(i) in the limit N-->infinity. We show that in some of the conformally invariant theories such as the simplest model 1/4 lambda p hi(4), the resonance can be terminated by the back reaction of produce d particles long before [chi(2)] or [phi(2)] become of the order phi(2 ). We analyze the changes in the theory of reheating in this model whi ch appear if the inflaton field has a mass m. In this case the conform al invariance is broken, and the resonance may acquire the features of stochasticity and intermittancy even if the mass is very small, so th at (m(2)/2)phi(2) much less than(lambda/4)phi(4). We give a classifica tion of different resonance regimes for various relations between the coupling constants, masses, and the amplitude of the oscillating infla ton field phi in a general class of theories +/-(m(2)/2)phi(2)+(lambda /4)phi(4)+(g(2)/2)phi(2) chi(2). [S0556-2821(97)05122-9].