Constraints on the scalar-field potential in warm inflation

We quantify the degree of fine-tuning required to achieve an observationally viable period of inflation in the strongly dissipative regime of warm inflation. The "fine-tuning" parameter A is taken to be the ratio of the change in the height of the potential Delta V to the change in the scalar field (Delta 0)4, i.e., the width of the potential, and therefore measures the requisite degree of flatness in the potential. The best motivated warm inflationary scenarios involve a dissipation rate of the kind Gamma proportional to Tc with c >= 0, and for all such cases, the bounds on A are tighter than those for standard cold inflation by at least 3 orders of magnitude. In other words, these models require an even flatter potential than standard inflation. On the other hand for the case of warm inflation with c < 0, we find that in a strongly dissipative regime the bound on A can significantly weaken with respect to cold inflation. Thus, if a warm inflation model can be constructed in a strongly dissipative, negatively temperature-dependent regime, it accommodates steeper potentials otherwise ruled out in standard inflation.