Warm hilltop inflation

We study the low-temperature limit of warm inflation in a hilltop model. This limit remains valid up to the end of inflation, allowing an analytic description of the entire inflationary stage. In the weak dissipative regime, if the kinetic density of the inflaton dominates after inflation, low-scale inflation is attained with Hubble scale as low as 1 GeV. In the strong dissipative regime, the model satisfies the observational requirements for the spectral index with a mild tuning of the model parameters, while also overcoming the $\eta$-problem of inflation. However, there is some danger of gravitino overproduction unless the particle content of the theory is large.

Figure 1

$\log C_{\varphi }$-$\log H$ plane in the weak dissipation limit. After the relevant scales leave the horizon, inflation is terminated by corrections of the potential $\delta V=-|V_n|{\varphi }^n$. The case shown corresponds to a correction term with $n=4$. The available parameter space (shaded area) is constrained by gravitino overproduction (using $T_{m_{3/2}}\equiv {10}^{7–9}\mathrm{GeV}$), the nucleosynthesis bound (using $T_{\mathrm{BBN}}\sim \mathrm{MeV}$), and the relic graviton abundance at nucleosynthesis, Eqs. (25, 26, 29), respectively. Consistency with warm inflation imposes a lower bound on the amount of dissipation, whereas the strong dissipation regime results in an upper bound, Eqs. (19, 21), respectively.

Figure 2

The figure shows the $\log C_{\varphi }$-$\log |\eta |$ plane. The light gray (light green) area represents the space where the thermal spectrum of perturbations matches the observed amplitude $N_{*}\sim 50$ $e$-foldings before the end of inflation, with ${\varphi }_{\mathrm{end}}<10m_P$. Within the dark gray (reddish) band, the resulting value of the spectral index is within the 1-$\sigma$ window: $n={0.960}_{-0.013}^{+0.014}$, as inferred by $\mathrm{WMAP}+\mathrm{BAO}+\mathrm{SN}$ data in the $\Lambda \mathrm{CDM}$ model for negligible tensor perturbations. In the graph lines of constant $H$ and $Q\equiv {\rm Y}/3H$ are also depicted.