First-Order Nonthermal Phase Transition after Preheating

Abstract

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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