Reexamination of the warm inflation curvature perturbations spectrum
  The two approaches to compute perturbations in warm inflation are examined.
It is shown that both approaches lead to different expressions for the
amplitude of the primordial spectrum, with a difference between them of
$\Upsilon/(4H)$ at leading order, where $\Upsilon$ is the dissipation
coefficient. In terms of observables, this discrepancy can lead to the spectral
index differing by up to order $\mathcal{O}(10^{-3})$, which is within
precision demands for current CMB data. Thus, it is important to resolve this
ambiguity to have reliable predictions from warm inflation. For this we prove
the extent of this discrepancies by deriving a formula for the spectral index
and the tensor-to-scalar ratio in each approach. In doing so, we find
disparities to be more noticeable in a regime where dissipation is comparable
with the expansion rate, which is a very important regime from a
phenomenological point of view. To determine the extent of the discrepancy,
several cases are examined, including quadratic, quartic and hybrid potentials
with quadratic and $T-$dependent dissipative coefficients. The origin of the
discrepancy is found to be due to the approximation performed in one of the
methods, which underestimates the variation of the momentum perturbation with
expansion. Once this is corrected, both approaches are then in agreement.
