Constraints on Axion Inflation from the Weak Gravity Conjecture

Abstract: We derive constraints facing models of axion inflation based on decay constant alignment from a string-theoretic and quantum gravitational perspective. In particular, we investigate the prospects for alignment and anti-alignment' of $C_4$ axion decay constants in type IIB string theory, deriving a strict no-go result in the latter case. We discuss the relationship of axion decay constants to the weak gravity conjecture and demonstrate agreement between our string-theoretic constraints and those coming from thegeneralized' weak gravity conjecture. Finally, we consider a particular model of decay constant alignment in which the potential of $C_4$ axions in type IIB compactifications on a Calabi-Yau three-fold is dominated by contributions from $D7$-branes, pointing out that this model evades some of the challenges derived earlier in our paper but is highly constrained by other geometric considerations.

• The paper demonstrates that quantum gravity limits hinder axion decay constant alignment for achieving super-Planckian inflation.
• It employs type IIB string theory frameworks to show that geometric constraints and multifield contributions restrict the effective field range.
• The study warns against oversimplified large-field models, urging careful consideration of moduli space and convex hull constraints in inflationary scenarios.

Constraints on Axion Inflation from the Weak Gravity Conjecture

In the exploration of cosmological inflation, axion models have gained prominence due to their capacity to address the large-field inflation paradigm, wherein the inflaton traverses a super-Planckian field range. This paper focuses on axion inflation constrained by string theory implications and the weak gravity conjecture (WGC). The analysis is rooted in type IIB string theory, emphasizing the role of axion decay constant alignment, a proposal advocated to evade traditional field range limitations.

The crux of the research is assessing the feasibility of achieving inflation through axion decay constant alignment, a mechanism aimed at extending the effective field range via geometric alignment of multiple axionic fields. This is particularly challenging under the restrictions imposed by the WGC—originally formulated to ensure the absence of stable black hole remnants through the existence of sufficiently light charged particles. The authors extend this conjecture’s application to axions, suggesting that inflaton field ranges substantially beyond the Planck scale might be improbable without contravening quantum gravity principles.

A significant finding is the derived no-go result for 'anti-alignment' of $C_4$ axion decay constants in type IIB string theory on Calabi-Yau three-fold compactifications. This is complemented by an analysis of the geometric constraints affecting decay constant alignment—revealing that even when this alignment appears to permit larger effective field ranges, underlying geometric interactions and additional contributions from other divisors typically constrain the field space metrics within theoretical limits. Moreover, despite potential paths through enhancements in moduli space metrics or extra decay constant alignment contributions, achieving sufficient enhancement remains theoretically and geometrically complex.

For a theoretical inflationary model, a determinant factor is ensuring that the moduli space radii, resultant from multi-field contributions, remain bounded. The generalized WGC implies that, even in multi-axion scenarios, simply aligning decay constants does not relax the super-Planckian traversal bounds due to the constraints on the convex hull formed by the associated charge vectors. This persistent hurdle suggests an intrinsic tension between achieving desired physical inflationary trajectories and the rigorous demands of consistent quantum gravity.

In practical terms, the paper discusses scenarios involving $D7$-branes, where gaugino condensation can alter potential contributions to axions and theorizes how manipulating these configurations could sidestep instanton-induced constraints, presenting new intriguing avenues, yet encumbered by constraints such as non-intersecting $D7$-branes—a requirement that limits viable alignment configurations within realistic compactifications.

The implications of this research are manifold: it advises caution in invoking axion-based large-field inflation models without considering their compatibility within quantum gravity frameworks, particularly concerning the generalized WGC. Additionally, it elucidates the challenges of embedding inflationary models within string theory, suggesting that alignment enhancements should not be simplistically presumed to overcome these fundamental barriers.

This analysis substantiates the rigors imposed by quantum gravitational corrections on cosmological models, pointing towards a selective filtration of inflationary scenarios that comply with higher-dimensional theoretical physics’ meta-constraints. Future advancements in non-perturbative string theoretic corrections or novel geometric constructions might provide enriched landscapes for axion inflation, but currently, the intersection of WGC with string-derived cosmology remains a restrictive but insightful domain, inviting further exploration.