We study the sensitivity of cosmological observables to the reheating phase following inflation driven by many scalar fields. We describe a method which allows semi-analytic treatment of the impact of perturbative reheating on cosmological perturbations using the sudden decay approximation. Focusing on $mathcal{N}$-quadratic inflation, we show how the scalar spectral index and tensor-to-scalar ratio are affected by the rates at which the scalar fields decay into radiation. We find that for certain choices of decay rates, reheating following multiple-field inflation can have a significant impact on the prediction of cosmological observables.
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