We present the first fully nonlinear calculation of inflaton decay. We map inflaton decay onto an equivalent classical problem and solve the latter numerically. In the lf 4 model, we find that parametric resonance develops slower and ends at smaller values of fluctuating fields, as compared to estimates existing in literature. We also observe a number of qualitatively new phenomena, including a stage of semiclassical thermalization, during which the decay of inflaton is essentially as effective as during the resonance stage. [S0031-9007 (96)00641-2] PACS numbers: 98.80.Cq, 05.70.FhAmplification of quantum fluctuations and transition to semiclassical behavior are familiar subjects in inflationary cosmology (for a review of the latter, see Ref.[1]). Semiclassical fluctuations produced during inflation can explain the observed large scale structure of the Universe [2]. The theory of their production is by now well developed; for a recent rather general presentation, see Ref.[3]. After inflation ends, the scalar field (inflaton) that was driving it begins to oscillate. These oscillations are thought to lead to particle production, inflaton decay, and eventually to reheating of the Universe.It was only recently realized that phenomena related to large occupation numbers of Bose particles produced by inflaton decay, such as parametric resonance, can be significant in the reheating process [4][5][6]. That means that semiclassical phenomena may play as important a role in reheating as they do in the structure formation. Of course, the eventual thermalized state will include modes with small occupation numbers, which are essentially quantal, but initial stages of the reheating process should admit a semiclassical description.However, semiclassical description of fluctuations produced by inflaton decay has not been obtained. The existing treatments of parametric amplification [4-6] employ the standard methods of analyzing particle production, based on Bogoliubov transformation. These methods allow one to take into account some of the backreaction effects of produced particles on the oscillating zero-momentum ͑k 0͒ mode, such as time dependence of the frequency of oscillations, but cannot reliably take into account many other nonlinear effects that become important certainly no later than the frequency change. These effects include scattering of produced particles off the k 0 mode, which knocks particles out of the k 0 state; rescattering of the produced particles, which populates nonresonant modes as well as returns particles back to k 0 (Bose condensation) [7], etc. We generically refer to these effects as rescattering; we will see that they begin as essentially classical interactions.Order of magnitude estimates of the amplitude squared of produced fluctuations ͑df͒ 2 at the end of the resonance stage were obtained in Refs. [4][5][6]. It is important to know ͑df͒ 2 more precisely, because in realistic inflationary models, its magnitude determines whether any symmetries are restored in the nonthermal regime after the reso...

We show that gravitational radiation is produced quite efficiently in interactions of classical waves created by resonant decay of a coherently oscillating field. For simple models of chaotic inflation in which the inflaton interacts with another scalar field, we find that today's ratio of energy density in gravitational waves per octave to the critical density of the universe can be as large as 10^{-12} at the maximal wavelength of order 10^{5} cm. In the pure $\lambda\phi^4$ model, the maximal today's wavelength of gravitational waves produced by this mechanism is of order 10^6 cm, close to the upper bound of operational LIGO and TIGA frequencies. The energy density of waves in this model, though, is likely to be well below the sensitivity of LIGO or TIGA at such frequencies. We discuss possibility that in other inflationary models interaction of classical waves can lead to an even stronger gravitational radiation background.Comment: Latex, 18 pages including 3 figure

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We present results of fully nonlinear calculations of decay of the inflaton interacting with another scalar field X. Combining numerical results for a cosmologically interesting range of the resonance parameter, q # 10 6 , with analytical estimates, we extrapolate them to larger q. We find that scattering of X fluctuations off the Bose condensate is a very efficient mechanism limiting growth of X fluctuations. For a single-component X, the resulting variance, at large q, is much smaller than that obtained in the Hartree approximation.[S0031-9007(97)03914-8]

We investigate nonthermal phase transitions that may occur after post-inflationary preheating in a simple model of a two-component scalar field with the effective potential $\lambda (\phi_i^2 - {\rm v}^2)^2/4$, where $\phi_1$ is identified with the inflaton field. We use three-dimensional lattice simulations to investigate the full nonlinear dynamics of the model. Fluctuations of the fields generated during and after preheating temporarily make the effective potential convex in the $\phi_1$ direction. The subsequent nonthermal phase transition with symmetry breaking leads to formation of cosmic strings even for ${\rm v} \gg 10^{16}$ GeV. This mechanism of string formation, in a modulated (by the oscillating field $\phi_{1}$) phase transition, is different from the usual Kibble mechanism.Comment: 6 pages, 7 figures, revtex. Computer generated movies illustrating string production can be found at http://www.physics.purdue.edu/~tkachev/movies.html and at http://physics.stanford.edu/~lind

During preheating after inflation, parametric resonance rapidly generates very large fluctuations of scalar fields. In models where the inflaton field φ oscillates in a double-well potential and interacts with another scalar field X, fluctuations of X can keep the φ → −φ symmetry temporarily restored. If the coupling of φ to X is much stronger than the inflaton self-coupling, the subsequent symmetry breaking is a first-order phase transition. We demonstrate the existence of this nonthermal phase transition with lattice simulations of the full nonlinear dynamics of the interacting fields. In particular, we observe nucleation of an expanding bubble.Cosmological phase transitions are one of the central topics of modern cosmology [1]. Recently, this theory was supplemented by the possibility of nonthermal cosmological phase transitions [2], i.e. phase transitions driven by fluctuations produced so rapidly that they did not have time to thermalize. Large nonthermal fluctuations naturally occur in inflationary models during preheating [3].Fluctuations of Bose fields generated by the parametric resonance during preheating have large occupation numbers and can be considered as interacting classical waves, which allows to study the dynamics of fluctuations during and after preheating using lattice simulations [4]. Numerical calculations, as well as analytical estimates [4][5][6][7][8][9][10][11] have shown that the maximal values achieved by fluctuations can be large enough to cause cosmologically interesting phase transitions. Nevertheless, until now there was no direct demonstration of the existence of such phase transitions; several groups which studied this issue numerically [12] either concentrated on models where phase transitions cannot occur, or neglected essential feedback effects such as rescattering of created particles.We have performed a number of lattice simulations of nonthermal phase transitions, which demonstrated formation of various types of topological defects [13]. In this Letter we report results that prove that nonthermal phase transitions may take place after preheating even on the scale as large as the GUT scale ∼ 10 16 GeV. The phase transition that we have found is first-order, which may have particularly important cosmological implications. First-order phase transitions have a very clear signature: they proceed through nucleation and subsequent expansion of a bubble of the new phase inside the old phase. In our opinion, the presence of this distinctive signature eliminates all doubts about the possibility of nonthermal phase transitions in the class of theories under investigation.As a prototype we will use the modelThe inflaton scalar field φ has a double-well potential and interacts with an N -component scalar field X;For simplicity, the field X is taken massless and without self-interaction. The fields couple minimally to gravity in a FRW universe with a scale factor a(t).The initial conditions at the beginning of preheating are determined by the preceding stage of inflation. One can define...

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