Viscous Warm Inflation: Hamilton-Jacobi formalism
  Using Hamilton-Jacobi formalism, The scenario of warm inflation with viscous
pressure is considered. The formalism gives a way of computing the slow-rolling
parameters without extra approximation, and it is well-known as a powerful
method in cold inflation. The model is studied in detail for three different
cases of dissipation and bulk viscous pressure coefficients. In the first case
where both coefficients are taken as a constant, it is shown that the case
could not portray warm inflationary scenario compatible with observational data
even it is possible to restrict the model parameters. For other cases, the
results shows that the model could properly predicts the perturbation
parameters in which they stay in perfect agreement with Planck data. As a
further argument, $r-n_s$ and $\alpha_s-n_s$ are drown that show the required
result could stand in acceptable area expressing a compatibility with
observational data.
