Reconstructing warm inflation

The reconstruction of a warm inflationary universe model from the scalar spectral index $n_S(N)$ and the tensor to scalar ratio $r(N)$ as a function of the number of e-folds $N$ is studied. Under a general formalism we find the effective potential and the dissipative coefficient in terms of the cosmological parameters $n_S$ and $r$ considering the weak and strong dissipative stages under the slow roll approximation. As a specific example, we study the attractors for the index $n_S$ given by $n_S-1\propto N^{-1}$ and for the ratio $r\propto N^{-2}$, in order to reconstruct the model of warm inflation. Here, expressions for the effective potential $V(\varphi )$ and the dissipation coefficient $\mathrm{\Gamma }(\varphi )$ are obtained.