Natural inflation with and without modulations in type IIB string theory

TL;DR

This paper proposes a string-theoretic realization of natural inflation in type IIB string theory on toroidal orientifolds, identifying the inflaton with the imaginary part of a complex structure modulus ${\rm Im}\,U^2$ and achieving a trans-Planckian axion decay constant through moduli-dependent one-loop threshold corrections to the gauge kinetic function. Moduli stabilization proceeds in two stages: flux-induced stabilization of $S$ and heavy complex structure combinations, followed by racetrack (or KKLT-like) non-perturbative stabilization of the Kähler modulus and remaining light moduli, yielding a light inflaton sector decoupled from heavy fields. The inflaton potential is generated by gaugino condensation and can take the standard natural inflation form $V_{\rm eff}=\Lambda_1\left(1-\cos(\lambda_1\phi)\right)$, with possible modulations $V_{\rm mod}=\Lambda_2\cos(\lambda_2\phi)$ arising from finite-loop corrections; these modulations can adjust predictions for the tensor-to-scalar ratio $r$ while keeping the scalar spectral index $n_s$ in agreement with Planck/WMAP data, providing a flexible framework that includes both unmodulated and modulated natural inflation. The work connects explicit stringy threshold corrections, via the Dedekind eta-function, to inflationary observables and outlines potential extensions to richer Calabi–Yau settings and reheating dynamics.

Abstract

We propose a mechanism for the natural inflation with and without modulation in the framework of type IIB string theory on toroidal orientifold or orbifold. We explicitly construct the stabilization potential of complex structure, dilaton and Kähler moduli, where one of the imaginary component of complex structure moduli becomes light which is identified as the inflaton. The inflaton potential is generated by the gaugino-condensation term which receives the one-loop threshold corrections determined by the field value of complex structure moduli and the axion decay constant of inflaton is enhanced by the inverse of one-loop factor. We also find the threshold corrections can also induce the modulations to the original scalar potential for the natural inflation. Depending on these modulations, we can predict several sizes of tensor-to-scalar ratio as well as the other cosmological observables reported by WMAP, Planck and/or BICEP2 collaborations.

Figures (3)

• Figure 1: Predictions of $(n_s, r)$ in the range of e-folding number, $50\leq N_e \leq 60$. For the universal value of $\langle{\rm Re}\,U^2\rangle=1$, black-solid, red-dashed, green-dashed, blue-dotdashed and orange-dotted lines correspond to the fixed ratios $b/L=1/10, 1/5, 1/4, 1/3, 1/2$, respectively.
• Figure 2: The behavior of the slow-roll parameters, $\epsilon$, $\eta$ and $\xi^2$, which correspond to black-dotdashed, red-dashed and blue-solid curves, respectively. In the left (right) panel, we set $b/L=1/5~(1/10)$ and $\langle{\rm Re}\,U^2\rangle =1.2~(2.4)$.
• Figure 3: The scalar potential $V$ versus the inflaton value $\phi$. Along with Fig. \ref{['fig:slowpara']}, the black-solid curve corresponds to the scalar potential (\ref{['eq:totinfpo']}) with modulations for the parameter $b/L=1/5$ and $\langle{\rm Re}\,U^2\rangle =1.2$. On the other hand, the red-dotted curve corresponds to the leading scalar potential (\ref{['eq:infpo']}) without modulations for the same parameters.