Evolution of the curvature perturbation during and after multi-field inflation

Abstract

We study the evolution of the curvature perturbation on the super-horizon scales starting from the inflationary epoch until there remains only a single dynamical degree of freedom, presureless matter, in the universe. We consider the cosmic inflation driven by a multiple number of the inflaton fields, which decay into both radiation and pressureless matter components. We present a complete set of the exact background and perturbation equations which describe the evolution of the universe throughout its history. By applying these equations to the simple but reasonable model of multi-field chaotic inflation, we explicitly show that the total curvature perturbation is continuously varying because of the non-adiabatic components of the curvature perturbation generated by the multiple inflaton fields throughout the whole evolution of the universe. We also provide an useful analytic estimation of the total as well as matter and radiation curvature perturbations, assuming that matter is completely decoupled from radiation from the beginning. The resulting isocurvature perturbation between matter and radiation is at most sub-percent level when the masses of the inflaton fields are distributed between $10^{-6}{m}_{pl}$ and $10^{-5}{m}_{pl}$. We find that this result is robust unless we use non-trivial decay rates, and that thus, in general, it is hard to obtain large matter-radiation isocurvature perturbation. Also, by using the $\delta N$ formalism, we point out that the inflationary calculation, especially when involving multiple inflaton fields, is likely to lose the potentially important post-inflationary evolution which can modify the resulting curvature perturbation.

arXiv comment31 pages, 6 figures, Final version to appear in JCAP. Add calculation of power spectrum and spectral index. We provide more discussion

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• Multifield inflation beyond $N_{\mathrm{field}}=2$: non-Gaussianities and single-field effective theory
• Reheating, Multifield Inflation and the Fate of the Primordial Observables
• Reheating and Dark Matter Freeze-in in the Higgs-$R^2$ Inflation Model
• Inflation in a two 3-form fields scenario
• Constraints on neutrino density and velocity isocurvature modes from WMAP-9 data
• Primordial curvature perturbation during and at the end of multi-field inflation
• Opening the reheating box in multifield inflation
• Primordial gravitational wave of BICEP2 from dynamical double hybrid inflation
• Covariant evolution of perturbations during reheating in two-field inflation
• Towards a warped inflationary brane scanning
• Entropy Perturbations in N-flation
• Curvaton mechanism after multi-field inflation