Aligned natural inflation with modulations

TL;DR

The paper shows that aligned natural inflation, when constrained by the weak gravity conjecture, generically acquires a subleading modulation of the inflaton potential, leading to an additional term $\Lambda_{ m mod}^{4}[1-\cos(\phi/f_{ m mod}+\delta)]$ atop the main potential $\Lambda_{ m eff}^{4}[1-\cos(\phi/f_{ m eff})]$ with $f_{ m eff} \gg M_{\rm Pl}$ and $f_{ m mod} < M_{\rm Pl}/S_{\rm ins}$. This modulation induces oscillations in the primordial curvature power spectrum: $P_{\cal R}(k) = P_{\cal R}^{(0)}(k)[1 + \delta n_s \cos(\phi_k/f_{\rm mod}+\beta)]$, where $\delta n_s$ is set by a perturbative parameter $b = \Lambda_{ m mod}^{4}/(V'_{0}(\phi_*) f_{\rm mod})$. Planck data constrain $(\Lambda_{\rm mod}/\Lambda_{\rm eff})^{4}$ to about $\mathcal{O}(10^{-4}-10^{-6})$ depending on $f_{\rm mod}$, with only modest effects on $r$ (\sim10% at most) but a broader viable $(n_s, r)$ region and small resonant non-Gaussianity $f_{NL}^{\rm res} \lesssim \mathcal{O}(1)$. Overall, the work links UV-mensible multi-axion inflation to observable CMB signatures, offering a path to test UV completions through detailed oscillatory features in the power spectrum.

Abstract

The weak gravity conjecture applied for the aligned natural inflation indicates that generically there can be a modulation of the inflaton potential, with a period determined by sub-Planckian axion scale. We study the oscillations in the primordial power spectrum induced by such modulation, and discuss the resulting observational constraints on the model.

Figures (4)

• Figure 1: The KNP alignment mechanism and the convex hull condition. The axion couplings $\vec{p}_1$ and $\vec{p}_2$ (blue arrows) are aligned to be nearly parallel to produce a super-Planckian effective decay constant. These couplings do not necessarily coincide with the instanton couplings $\vec{q}_1$ and $\vec{q}_2$ required by the weak gravity conjecture. Here we assume $\vec{q}_1=\vec{p}_1$, and therefore $\vec{q}=\vec{q}_2$ (black arrow).
• Figure 2: Parameter region on the plane of ($f_{\rm mod}, \delta n_s$) with 68% (pink) and 95% (light pink) CL likelihood with respect to the Planck data on the temperature anisotropy and low-$\ell$ polarization. The dashed lines represent the predictions from the inflaton potential (\ref{['inf_pot']}) with $(\Lambda_{\rm mod}/\Lambda_{\rm eff})^4 = 10^{-5},\, 5\times 10^{-6},\, 10^{-6}$ from the top to the bottom. The shaded region in the upper left corner corresponds to the region that our perturbative approach for modulation becomes unreliable as the expansion parameter $b$ is not small enough, e.g. $b \geq 0.3$ for gray region and $b\geq 0.5$ for dark gray region.
• Figure 3: $95\%$ CL upper bound on $(\Lambda_{\rm mod}/\Lambda_{\rm eff})^4$ as a function of $f_{\rm mod}$ for $f_{\rm eff} = 5M_{\rm Pl} \textrm{ (red)}$, $\,10M_{\rm Pl} \textrm{ (blue)}$ and $20M_{\rm Pl}$ (green).
• Figure 4: Green bands represent $(n_s^{(0)}, r)$ predicted by natural inflation with modulations, i.e. the inflaton potential (\ref{['inf_pot']}), while the yellow lines are the results in the absence of modulation. The red contours represent the model-independent 68% and 95% CL ranges of $(n_s^{(0)}, r)$, which are compatible with the observed CMB data fitted with the curvature power spectrum (\ref{['OscPS']}) including an oscillatory piece. The blue contours are the results of data fitting in the absence of oscillation, i.e. $\delta n_s=0$.