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Preheating after N-flation

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Preheating after N-flation

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  1. Abstract: We study preheating in N-flation, assuming the Marcenko-Pastur mass distribution, equal-energy initial conditions at the beginning of inflation and equal axion-matter couplings, where matter is taken to be a single, massless bosonic field. By numerical analysis we find that preheating via parametric resonance is suppressed, indicating that the old theory of perturbative preheating is applicable. While the tensor-to-scalar ratio, the non-Gaussianity parameters and the scalar spectral index computed for N-flation are similar to those in single-field inflation (at least within an observationally viable parameter region), our results suggest that the physics of preheating can differ significantly from the single-field case. Introduction Dynamics of N-flation N-flation[1] is a specific realization of multi-field inflation motivated by KKLT compactification of type IIB string theory. Advantages of this model are that the initial values of inflaton fields can be chosen to be sub-Planckian, and that the mass spectrum of inflatons is calculable under some assumptions. Observable cosmological imprints (the tensor-to-scalar ratio, the non-Gaussianity parameter and the spectral index) have been computed and are found to be similar to single-field inflation. While this suggests that N-flation is compatible with current observational data, it also means one cannot distinguish N-flation from standard inflation by these data alone. • Initial conditions • We assume equal-energy initial conditions at the onset of inflation: Preheating after N-flation • An advantage of N-flation is possibility to avoid super-Planckian initial conditions. So we shall set • Slow-roll conditions (1) for each inflaton and (2) for the whole system, where • We study the process of preheating for this model. Result: it is very different from the single-field case. The conditions (1) are violated for heavy inflatons first, even when the whole system still undergoes inflation. Shinsuke Kawai (Helsinki Institute of Physics, University of Helsinki) PRD77(2008)123507 [arXiv:0803:0321] with D. Battefeld • Light axion dominance By the time the slow-roll parameter for the whole system (2) becomes of order unity, heavy axions are settled down at the bottom of the potential and become negligible. This is due to: Mass spectrum of inflatons • The Lagrangian • The MP law prescribes the majority of the axions to be distributed around the lightest mass • Heavy fields start from smaller values due to where : hundreds ~ thousands the equal-energy initial conditions • Easther and McAllister[2] proposed Marcenko-Pastur distribution of inflaton masses (based on random matrix): • Heavy fields undergo overdamped evolution as the Hubble parameter is still large when they exit slow-roll regime (from renormalization of Newton’s const) (COBE normalization) • Analytic solutions The slow-roll approximation yields analytic solutions for the field evolution: • Inflatons (axions) interact only through gravity • We use rescaled mass parameter which together with the initial conditions describe the axions during N-flation. Because of the light axion dominance this approximation is valid before preheating commences, provided the heavy fields are ignored.

  2. Preheating after inflation • The model of preheating • N-flation with MP mass distribution We will model preheating with a single massless bosonic field coupled to the axions via the same coupling strength. The Lagrangian is In N-flation with MP-mass distribution the collective behavior of axions is not coherent (the oscillation of each field being dephased due to mass differences), leading to suppression of resonance. • In short time scales The time evolution of the matter field. While there is some enhancement due to parametric resonance, the overall amplitude decreases as the enhancement is not strong enough to overcome the dilution due to cosmic expansion. The parameters are chosen so that the single-filed model (the left column) is recovered if we set all the masses to be equal. The oscillating part of the matter mass term (to be compared with the bottom panel of the left column). The oscillations are blunt due to the relative mass differences of the axions. The adiabaticity parameter which indicates the strength of resonance effect (when its modulus is large the system is less adiabatic and particles may be produced due to the resonance effect). In the equal-mass case it oscillates with amplitude larger than 1, so we can see the resonance effect is extremely weak in the MP case. Choose (sufficient e-folding) and use only the lightest 10%, , for the preheating computation (justified by the light axion dominance) • Ignoring backreaction (justified below), the EOM are (3) • Equal-mass = single-field model (for comparison) When the masses of the axions are all equal, the multi-field model reduces to a single-field model, by setting ; Eqn (3) becomes • In long time scales It is well known that this system exhibits parametric resonance[3], driven by the oscillating inflaton. The time evolution of the matter field, in longer scales (time is measured in units of ). There is a burst around  The comoving occupation number computed for the comoving matter field X. The particle number increases at the burst, but such bursts are not frequent enough to overcome the dilution due to cosmic expansion. The oscillating part of the mass term, showing beats due to oscillating axions. The adiabaticity parameter, in longer time scales than above. The burst occurs at one of the peaks, but not at every peak (note that inclusion of cosmic expansion renders the resonance effect stochastic). The time evolution of the matter field. Cosmic expansion causes occasional decreases of the amplitude (stochastic resonance). The time evolution of the comoving particle number defined by where and (the bottom panel) The oscillating part of the mass term that drives the resonance. • Increasing the number of inflatons (with the same masses) does not change the resonance effect since it is equivalent to the single-field model of inflation. • Summary of the results In N-flation with MP mass distribution, the resonance effect is weak in short time scales and not frequent in long time scales. Consequently, the old theory of perturbative reheating applies to this scenario. References [1] Dimopoulos, Kachru, McGreevy, Wacker, arXiv:hep-th/0507205 [2] Easther, McAllister, JCAP 05 (2006) 018 [3] Kofman, Linde, Starobinsky, Phys. Rev. D 56 (1997) 3258 See the paper for the complete list.

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