1997/05/19 by Patrick B. Greene, Patrick Greene, Lev Kofman +3 · 9 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Combinatorics #Cosmology and Gravitation Theories #Coupling (piping) #Geophysics and Gravity Measurements #Lambda #Limiting #Mathematical physics #Mathematics #Physics #Quantum mechanics #Resonance (particle physics) #Solar and Space Plasma Dynamics #astro-ph #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.56.6175
published as Phys.Rev.D56:6175-6192,1997 · 19 pages, revtex, 12 figures
arxiv created 1997/05/19 · openalex publication_date 1997/11/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider preheating in the theory (1)/(4)\ensuremathλ\ensuremathφ4+(1)/(2)g2\ensuremathφ2\ensuremathχ2, where the classical oscillating inflaton field \ensuremathφ(t) decays into \ensuremathχ particles and \ensuremathφ particles. The parametric resonance which leads to particle production in this conformally invariant theory is described by the Lam'e equation. It significantly differs from the resonance in the theory with a quadratic potential. The structure of the resonance depends in a rather nontrivial way on the parameter g2/\ensuremathλ. We find an ``unnatural selection'' rule: the most efficient creation of particles occurs not for particles which have the strongest coupling to the inflaton field, but for those which have the greatest characteristic exponent \ensuremathμ. We construct the stability-instability chart in this theory for arbitrary g2/\ensuremathλ. We give simple analytic solutions describing the resonance in the limiting cases g2/\ensuremathλ\ensuremath≪1 and g2/\ensuremathλ\ensuremath≫1, and in the theory with g2=3\ensuremathλ, and with g2=\ensuremathλ. From the point of view of parametric resonance for \ensuremathχ, the theories with g2=3\ensuremathλ and with g2=\ensuremathλ have the same structure, respectively, as the theory (1)/(4)\ensuremathλ\ensuremathφ4, and the theory (\ensuremathλ/4N)(\ensuremathφi2)2 of an N-component scalar field \ensuremathφi in the limit N\ensuremath→\ensuremath∞. We show that in some of the conformally invariant theories such as the simplest model (1)/(4)\ensuremathλ\ensuremathφ4, the resonance can be terminated by the back reaction of produced particles long before 〈\ensuremathχ2〉 or 〈\ensuremathφ2〉 become of the order \ensuremathφ2. We analyze the changes in the theory of reheating in this model which appear if the inflaton field has a mass m. In this case the conformal invariance is broken, and the resonance may acquire the features of stochasticity and intermittancy even if the mass is very small, so that (m2/2)\ensuremathφ2\ensuremath≪(\ensuremathλ/4)\ensuremathφ4. We give a classification of different resonance regimes for various relations between the coupling constants, masses, and the amplitude of the oscillating inflaton field \ensuremathφ in a general class of theories \ifmmode±\else\textpm\fi(m2/2)\ensuremathφ2+(\ensuremathλ/4)\ensuremathφ4+(g2/2)\ensuremathφ2\ensuremathχ2.