Multi-Natural Inflation

Abstract

We propose a multi-natural inflation model in which the single-field inflaton potential consists of two or more sinusoidal potentials that are comparable in size, but have different periodicity with a possible non-zero relative phase. The model is versatile enough to realize both large-field and small-field inflation. We show that, in a model with two sinusoidal potentials, the predicted values of the spectral index and tensor-to-scalar ratio lie within the $1σ$ region of the Planck data. In particular, there is no lower bound on the decay constants in contrast to the original natural inflation. We also show that, in a certain limit, multi-natural inflation can be approximated by a hilltop quartic inflation model.

Figures (4)

• Figure 1: Left: the prediction of $(n_s, r)$ of multi-natural inflation for three different values of $\Lambda_2^4$. Solid (dashed) lines correspond to the e-folding number $N=60$ ($N=50$). Right: the corresponding inflaton potentials. The red dots represent the position at horizon crossing at $N= 60$ for the case of $B=0.40$.
• Figure 2: Same as Fig. \ref{['fig:nsr1']} but for different values of the relative phase $\theta$.
• Figure 3: Behavior of $n_s$ (left) and $r$ (right) as a function of $f$. The shaded regions in the left figure correspond to 1 and 2$\sigma$ allowed regions for $n_s$ from Planck data. The shaded region on the right corresponds to the 95% CL for $r$ ($r < 0.11$).
• Figure 4: Planck normalized values for $\Lambda$ (left) and $m_\phi$ (right) as a function of $f$.