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      Structure of Resonance in Preheating after Inflation

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          Abstract

          We consider preheating in the theory \(1/4 \lambda \phi^4 + 1/2 g^2\phi^2\chi^2 \), where the classical oscillating inflaton field \(\phi\) decays into \(\chi\)-particles and \(\phi\)-particles. The parametric resonance which leads to particle production in this conformally invariant theory is described by the Lame 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 \(g^2/\lambda\). We construct the stability/instability chart in this theory for arbitrary \(g^2/\lambda\). We give simple analytic solutions describing the resonance in the limiting cases \(g^2/\lambda\ll 1\) and \(g^2/\lambda \gg 1\), and in the theory with \(g^2=3\lambda\), and with \(g^2 =\lambda\). From the point of view of parametric resonance for \(\chi\), the theories with \(g^2=3\lambda\) and with \(g^2 =\lambda\) have the same structure, respectively, as the theory \(1/4 \lambda \phi^4\), and the theory \(\lambda /(4 N) (\phi^2_i)^2\) of an N-component scalar field \(\phi_i\) in the limit \(N \to \infty\). We show that in some of the conformally invariant theories such as the simplest model \(1/4 \lambda\phi^4\), the resonance can be terminated by the backreaction of produced 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 which appear if the inflaton field has a small mass.

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          Reheating after Inflation

          The theory of reheating of the Universe after inflation is developed. The transition from inflation to the hot Universe turns out to be strongly model-dependent and typically consists of several stages. Immediately after inflation the field \(\phi\) begins rapidly rolling towards the minimum of its effective potential. Contrary to some earlier expectations, particle production during this stage does not lead to the appearance of an extra friction term \(\Gamma\dot\phi\) in the equation of motion of the field \(\phi\). Reheating becomes efficient only at the next stage, when the field \(\phi\) rapidly oscillates near the minimum of its effective potential. We have found that typically in the beginning of this stage the classical inflaton field \(\phi\) very rapidly (explosively) decays into \(\phi\)-particles or into other bosons due to broad parametric resonance. This stage cannot be described by the standard elementary approach to reheating based on perturbation theory. The bosons produced at this stage, as well as some part of the classical field \(\phi\) which survives the stage of explosive reheating, should further decay into other particles, which eventually become thermalized. The last stages of decay can be described in terms of perturbation theory. Complete reheating is possible only in those theories where a single massive \(\phi\)-particle can decay into other particles. This imposes strong constraints on the structure of inflationary models. On the other hand, this means that a scalar field can be a cold dark matter candidate even if it is strongly coupled to other fields.
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            Universe Reheating after Inflation

            We study the problem of scalar particle production after inflation by a rapidly oscillating inflaton field. We use the framework of the chaotic inflation scenario with quartic and quadratic inflaton potentials. 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 \(V(\varphi) = \lambda \varphi^4\), the particle production process is very efficient even for small values of coupling constants. The reheating temperature of the universe in this case is \(\left[\lambda\, \log\, (1/\lambda) \right]^{- 1}\) 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 other scalar field 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 (see e.g. Ref. 13), 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.
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              Non-Thermal Phase Transitions after Inflation

              At the first stage of reheating after inflation, parametric resonance may rapidly transfer most of the energy of an inflaton field \(\phi\) to the energy of other bosons. We show that quantum fluctuations of scalar and vector fields produced at this stage are much greater than they would be in a state of thermal equilibrium. This leads to cosmological phase transitions of a new type, which may result in a copious production of topological defects and in a secondary stage of inflation after reheating.
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                Author and article information

                Journal
                19 May 1997
                Article
                10.1103/PhysRevD.56.6175
                hep-ph/9705347
                f7cd8356-078c-4d71-80c4-c431f8bb41ed
                History
                Custom metadata
                SU-ITP-97-19 and IfA-97-29
                Phys.Rev.D56:6175-6192,1997
                19 pages, revtex, 12 figures
                hep-ph astro-ph gr-qc hep-th

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