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 $\lambda$ is taken to be the ratio of
the change in the height of the potential $\Delta V$ to the change in the
scalar field $(\Delta \phi)^{4}$, 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
$\Gamma\propto T^c$ with $c\geq 0$, and for all such cases, the bounds on
$\lambda$ 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 $\lambda$ 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.
