Universe reheating after inflation

We study the problem of scalar particle production after inflation by an inflaton field which is oscillating rapidly relative to the expansion of the universe. We use the framework of the chaotic inflation scenario with quartic and quadratic inflaton potentials. Particles produced are described by a quantum scalar field χ, which is coupled to the inflaton via linear and quadratic couplings. The particle production effect is studied using the standard technique of Bogolyubov transformations. Particular attention is paid to parametric resonance phenomena which take place in the presence of the quickly oscillating inflaton field. We have found that in the region of applicability of perturbation theory the effects of parametric resonance are crucial, and estimates based on first-order Born approximation often underestimate the particle production. In the case of the quartic inflaton potential V(cphi)=λ${\mathit{cphi}}^4$, the particle production process is very efficient for either type of coupling between the inflaton field and the scalar field χ even for small values of coupling constants. The energy density of the universe after the decay of the inflaton oscillations is in this case a factor [λ ln(1/λ)${]}^{\mathrm{-}1}$ times larger than the corresponding estimates based on first-order Born approximation. In the case of the quadratic inflaton potential the reheating process depends crucially on the type of coupling between the inflaton and the scalar field χ and on the magnitudes of the coupling constants. If the inflaton coupling to fermions and its linear (in inflaton field) coupling to scalar fields are suppressed, then, as previously discussed by Kofman, Linde, and Starobinsky, the inflaton field will eventually decouple from the rest of the matter, and the residual inflaton oscillations may provide the (cold) dark matter of the universe. In the case of the quadratic inflaton potential we obtain the lowest and the highest possible bounds on the effective energy density of the inflaton field when it freezes out.