Tuning and Backreaction in F-term Axion Monodromy Inflation

TL;DR

This work investigates large-field inflation via F-term axion monodromy in string theory, emphasizing backreaction from complex-structure moduli. It shows a no-go for CY threefold orientifolds at weak coupling, and advocates CY fourfolds with a partial large complex structure regime, where the inflaton mass coefficient a(z) can be tuned while depending on other moduli. The authors derive an analytic form for the backreacted inflaton potential, show that a controlled quadratic regime can persist over a substantial field range under appropriate tunings, and validate these findings with numerical models including 3- and 4-moduli examples. They also estimate the impact of landscape tuning on the number of admissible flux vacua, finding that a large, non-negligible fraction can remain, keeping large-field inflation as a promising avenue in string theory, albeit with significant tuning and LVS considerations to manage Kähler moduli backreaction and uplift.

Abstract

We continue the development of axion monodromy inflation, focussing in particular on the backreaction of complex structure moduli. In our setting, the shift symmetry comes from a partial large complex structure limit of the underlying type IIB orientifold or F-theory fourfold. The coefficient of the inflaton term in the superpotential has to be tuned small to avoid conflict with Kahler moduli stabilisation. To allow such a tuning, this coefficient necessarily depends on further complex structure moduli. At large values of the inflaton field, these moduli are then in danger of backreacting too strongly. To avoid this, further tunings are necessary. In weakly coupled type IIB theory at the orientifold point, implementing these tunings appears to be difficult if not impossible. However, fourfolds or models with mobile D7-branes provide enough structural freedom. We calculate the resulting inflaton potential and study the feasibility of the overall tuning given the limited freedom of the flux landscape. Our preliminary investigations suggest that, even imposing all tuning conditions, the remaining choice of flux vacua can still be large enough for such models to provide a promising path to large-field inflation in string theory.

Figures (6)

• Figure 1: 'Naive' inflaton potential (dashed red line) and a possible effective inflaton potential after backreaction is taken into account (solid blue line). Note that the effective inflaton potential is not automatically sufficiently flat over transplanckian regions to realise large field inflation.
• Figure 2: Total potential \ref{['eq:inflationarylvs']} as a function of the volume $\mathcal{V}\sim e^{A}|a| \Delta y$. The dashed line intersects the potential at its maximum. Inflation could take place in the region on the left of the extremum. We normalised the $x$-axis such that $\langle \mathcal{V}\rangle=1$.
• Figure 3: Plots of the displacements $\delta x$ (blue, solid), $\delta v^1$ (red, long dashes), $\delta w^1$ (ochre, short dashes), $\delta v^2$ (green, dotted) and $\delta w^2$ (brown, dot-dashed) vs. $\Delta y$.
• Figure 4: Plots of the effective inflaton potential (blue, solid) and the 'naive' inflaton potential (red, dashed) vs. $\Delta y$.
• Figure 5: Plots of the displacements $\delta x$ (blue), $\delta v^1$ (red), $\delta w^1$ (ochre), $\delta v^2$ (green), $\delta w^2$ (brown), $\delta v^3$ (orange) and $\delta w^3$ (cyan) vs. $\Delta y$.