Multi-Natural Inflation in Supergravity

TL;DR

The paper demonstrates that multi-natural inflation can be realized within 4D ${\cal N}=1$ supergravity using an axion inflaton controlled by two sinusoidal potentials with a tunable relative phase, which can lift the spectral index into better agreement with Planck data while keeping the tensor-to-scalar ratio small. It provides a concrete SUGRA setup with saxion stabilization and a light axion, and develops a UV completion via a string-inspired model in which heavy moduli are stabilized and the axion remains the inflaton. The relative phase between the sinusoidal terms is key to adjusting $n_s$ without spoiling slow-roll, and a consistent picture emerges in which the inflation scale $H_{\rm inf}$ is below the gravitino mass, avoiding moduli destabilization. The framework also addresses reheating and baryogenesis through non-thermal leptogenesis, linking inflation to late-Universe cosmology within a UV-complete setting.

Abstract

We show that the recently proposed multi-natural inflation can be realized within the framework of 4D ${\cal N}=1$ supergravity. The inflaton potential mainly consists of two sinusoidal potentials that are comparable in size, but have different periodicity with a possible non-zero relative phase. For a sub-Planckian decay constant, the multi-natural inflation model is reduced to axion hilltop inflation. We show that, taking into account the effect of the relative phase, the spectral index can be increased to give a better fit to the Planck results, with respect to the hilltop quartic inflation. We also consider a possible UV completion based on a string-inspired model. Interestingly, the Hubble parameter during inflation is necessarily smaller than the gravitino mass, avoiding possible moduli destabilization. Reheating processes as well as non-thermal leptogenesis are also discussed.

Figures (6)

• Figure 1: The saxion potential for $A=2.3\times 10^{-12},~B=A/4,~a=2\pi/10,~b=2\pi/5,~f=0.1$ and $W_0=10^{-4}$. We have set $\varphi = 0$. The dashed (blue) line shows the saxion potential without the uplifting potential; the saxion is stabilized at $\sigma \sim \pm 5$, where the vacuum energy $3|W_0|^2$ is added for visualization purpose. The saxion can be stabilized near the origin if the sequestered uplifting potential $\Delta V$ is added, as shown by the solid (red) line.
• Figure 2: The scalar potential for the saxion and the axion (left) and the axion potential at the section of $\left\langle \sigma \right\rangle = 0$ (right). In the left panel, we show the logarithm of the scalar potential for the visualization purpose. We use the same model parameters as in Fig. \ref{['fig1']}. For comparison, the case with $B=0$ is also shown by the dashed (blue) line in the right panel.
• Figure 3: The scalar potential for the saxion and the axion (left) and the axion potential at the section of $\left\langle \sigma \right\rangle = 0$ (right) similarly to Fig.\ref{['fig2']}. We use $A=4.0\times 10^{-11},~ B=(6/7)^2 A,~a=\pi/7,~b=\pi/6,~f=0.1,~W_0=10^{-4}$ and $\theta=-7\pi/6$. The case with $B=0$ is also shown by the dashed (blue) line in the right panel, where the minima are chosen to coincide for visualization purposes.
• Figure 4: Plots of $n_s$ (left) and $r$ (right) for varying values of $B$ and $\theta$ for fixed decay constants $f_1 = 0.5$ and $f_2 = 0.45$, which corresponds to the case of $f_1 \approx f_2$ studied in the text. The green shaded region corresponds to the 2$\sigma$ allowed region for $n_s$ from the Planck data.
• Figure 5: Plots of $n_s$ (left) and $r$ (right) as a function of $f/M_p$. In the left figure, $\Theta \equiv \theta + \pi f_1/f_2$. In the right figure, there was no significant difference in the behavior of $r$ for the two values of $\Theta$, hence we chose $\Theta = -4.1\times 10^{-5}$. Solid (dotted) lines correspond to $N_e=60$ ($N_e=50$).