Higgs-otic Inflation and Moduli Stabilization

TL;DR

The paper tackles stabilizing all closed-string moduli while realizing large-field inflation via the Higgs-otic open-string inflaton. It develops an $ N=1$ supergravity framework incorporating ISD and IASD fluxes, DBI-induced kinetic terms, and KKLT-like stabilization, and analyzes backreaction on both the inflaton potential and its kinetics. The main result is that integrating out heavy Kähler moduli produces a controlled flattening of the inflaton potential, with an additional flattening from the DBI-related kinetic term; complex-structure backreaction can be suppressed through flux tuning, allowing trans-Planckian excursions and viable 60 $e$-folds consistent with CMB data. The study further demonstrates that well-chosen flux configurations can keep all moduli stabilized during inflation, yielding robust predictions for the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ within current observational bounds, while highlighting the ongoing need to reconcile flux tuning with global compactification constraints.

Abstract

We study closed-string moduli stabilization in Higgs-otic inflation in Type IIB orientifold backgrounds with fluxes. In this setup large-field inflation is driven by the vacuum energy of mobile D7-branes. Imaginary selfdual (ISD) three-form fluxes in the background source a $μ$-term and the necessary monodromy for large field excursions while imaginary anti-selfdual (IASD) three-form fluxes are sourced by non-perturbative contributions to the superpotential necessary for moduli stabilization. We analyze Kähler moduli stabilization and backreaction on the inflaton potential in detail. Confirming results in the recent literature, we find that integrating out heavy Kähler moduli leads to a controlled flattening of the inflaton potential. We quantify the flux tuning necessary for stability even during large-field inflation. Moreover, we study the backreaction of supersymmetrically stabilized complex structure moduli and the axio-dilaton in the Kähler metric of the inflaton. Contrary to previous findings, this backreaction can be pushed far out in field space if a similar flux tuning as in the Kähler sector is possible. This allows for a trans-Planckian field range large enough to support inflation.

Figures (10)

• Figure 1: Effective inflaton potential obtained analytically via the second-order expansion in $\delta t(\varphi)$ (orange line) and numerically to all orders (green dashed line), in comparison with the naive quadratic potential (blue line). The flattening effect of integrating out $T$ is evident. The orange curve is obtained from the result \ref{['eq:veff2']} with all higher-order terms in $(\alpha t_0)^{-1}$ taken into account.
• Figure 2: Scalar potential in the $t-\varphi$ plane. Evidently, the initial conditions must be very fine-tuned to allow for 60 $e$-folds of slow-roll inflation without destabilizing $t$.
• Figure 3: Contour plot of the original scalar potential $V(h,H)$ from Ibanez:2014swa (left panel) compared to effective scalar potential after moduli stabilization (right panel) for the parameter choice \ref{['eq:toypar2']}. Warmer color means a larger value of $V$. The darkest blue is the local minimum at $h = H = V = 0$. As expected, the direction $H$ is much steeper than the direction $h$, which is the inflaton direction. In the right panel local maxima are visible at $H=0$ and $|h_\text{c}| \approx 23$, the point at which the effective theory breaks down and the modulus is destabilized. We have plotted the effective potential \ref{['eq:v7']} to all orders in $\alpha t_0$ and $H$, and up to fourth order in $h$. In the case presented here, 60 $e$-folds of slow-roll inflation are possible along the trajectory $H = 0$. The single-field inflaton potential in that slice is identical to the orange line of Figure \ref{['fig:veff2']}.
• Figure 4: Effective scalar potential for the parameter choice \ref{['eq:toypar4']}. Naive quadratic potential (blue line) in comparison with effective inflaton potential for $\varphi$ (orange line) and numerical effective potential for the canonical variable in \ref{['result']}. The string scale is chosen too large for the DBI-induced flattening to have an effect.
• Figure 5: Effective scalar potential for the parameter choice \ref{['eq:toypar5']}. Naive quadratic potential (blue line) in comparison with effective inflaton potential for $\varphi$ (orange line) and numerical effective potential for the canonical variable in \ref{['result']}. In this case the additional flattening from the kinetic term is clearly visible.