Constraints on the scalar-field potential in warm inflation

Abstract

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