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Register a new userGeneral Relativistic effects in preheating
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Authors
Bruce A. Bassett
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General relativistic effects in the form of metric perturbations are usually neglected in the preheating era that follows inflation. We argue that in realistic multi-field models these effects are in fact crucial, and the fully coupled system of metric and quantum field fluctuations needs to be considered. Metric perturbations are resonantly amplified, breaking the scale-invariance of the primordial spectrum, and in turn stimulate scalar field resonances via gravitational rescattering. This non-gravitationally dominated nonlinear growth of gravitational fluctuations may have significant effects on the Doppler peaks in the cosmic background radiation, primordial black hole formation, gravitational waves and nonthermal symmetry restoration.
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Can super-Hubble metric perturbations be amplified exponentially during preheating ? Yes. An analytical existence proof is provided by exploiting the conformal properties of massless inflationary models. The traditional conserved quantity zeta is non-conserved in many regions of parameter space. We include backreaction through the homogeneous parts of the inflaton and preheating fields and discuss the role of initial conditions on the post-preheating power-spectrum. Maximum field variances are strongly underestimated if metric perturbations are ignored. We illustrate this in the case of strong self-interaction of the decay products. Without metric perturbations, preheating in this case is very inefficient. However, metric perturbations increase the maximum field variances and give alternative channels for the resonance to proceed. This implies that metric perturbations can have a large impact on calculations of relic abundances of particles produced during preheating.
We study thermal equilibration after preheating in inflationary cosmology, which is an important step towards a comprehensive understanding of cosmic thermal history. By noticing that the problem is parallel to thermalization after a relativistic heavy ion collision, we make use of the methods developed in this context and that seek for an analytical approach to the Boltzmann equation. In particular, an exact solution for number-conserving scatterings is available for the distribution function in a Friedmann-Lema^{i}tre-Robertson-Walker metric and can be utilized for the spectral evolution of kinetic equilibration process after preheating. We find that thermal equilibration is almost instantaneous on the time scale of the Hubble time. We also make an explicit prediction for the duration (the number of e-folds of expansion) required for this process of thermal equilibration to complete following the end of inflation.
Fermion creation during preheating in the presence of multiple scalar fields exhibits a range of interesting behaviour relevant to estimating post-inflation gravitino abundances. We present non-perturbative analysis of this phenomenon over a 6-dimensional parameter space in an expanding background paying particular attention to the interplay between instant and direct fermion preheating. In the broad resonance regime we find that instant fermion production is sensitive to suppression of the long wavelength scalar field modes during inflation. Further, the standard scenario of resonant fermionic preheating through inflaton decay can be significantly modified by instant preheating, and may even lead to a decrease in the number of fermions produced. We explicitly include the effects of metric perturbations and demonstrate that they are important at small coupling but not at strong coupling, due to the rapid saturation of the Pauli bound.
We investigate preheating in a higher-dimensional generalized Kaluza-Klein theory with a quadratic inflaton potential $V(phi)=frac12 m^2phi^2$ including metric perturbations explicitly. The system we consider is the multi-field model where there exists a dilaton field $sigma$ which corresponds to the scale of compactifications and another scalar field $chi$ coupled to inflaton with the interaction $frac12 g^2phi^2chi^2+tilde{g}^2phi^3chi$. In the case of $tilde{g}=0$, we find that the perturbation of dilaton does not undergo parametric amplification while the $chi$ field fluctuation can be enhanced in the usual manner by parametric resonance. In the presence of the $tilde{g}^2phi^3chi$ coupling, the dilaton fluctuation in sub-Hubble scales is modestly amplified by the growth of metric perturbations for the large coupling $tilde{g}$. In super-Hubble scales, the enhancement of the dilaton fluctuation as well as metric perturbations is weak, taking into account the backreaction effect of created $chi$ particles. We argue that not only is it possible to predict the ordinary inflationary spectrum in large scales but extra dimensions can be held static during preheating in our scenario.
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