Perturbative Reheating After Multiple-Field Inflation: The Impact on Primordial Observables

Abstract

We study the impact of perturbative reheating on primordial observables in models of multiple-field inflation. By performing a sudden decay calculation, we derive analytic expressions for the local-type non-linearity parameter $f_{\mathrm{NL}}^{\mathrm{local}}$, the scalar spectral index $n_{\zeta }$, and the tensor-to-scalar ratio $r_T$ as functions of the decay rates of the inflationary fields. We compare our analytic results to a fully numerical classical field theory simulation, finding excellent agreement. We find that the sensitivity of $f_{\mathrm{NL}}$, $n_{\zeta }$, and $r_T$ to the reheating phase depends heavily on the underlying inflationary model. We quantify this sensitivity, and discuss conditions that must be satisfied if observable predictions are to be insensitive to the dynamics of reheating. We demonstrate that upon completion of reheating, all observable quantities take values within finite ranges, the limits of which are determined completely by the conditions during inflation. Furthermore, fluctuations in both fields play an important role in determining the full dependence of the observables on the dynamics of reheating. By applying our formalism to two concrete examples, we demonstrate that variations in $f_{\mathrm{NL}}$, $n_{\zeta }$, and $r_T$ caused by changes in reheating dynamics are well within the sensitivity of Planck, and as such the impact of reheating must be accounted for when making predictions for models of multiple-field inflation. Our final expressions are very general, encompassing a wide range of two-field inflationary models, including the standard curvaton scenario. Our results allow a much more unified approach to studying two-field inflation including the effects of perturbative reheating. As such, entire classes of models can be studied together, allowing a more systematic approach to gaining insight into the physics of the early universe through observation.

v2: Updated to match published version, references added, typos corrected, appendix moved to main body of text. 26 pages, 7 figures

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