Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation

Abstract: In this note we show that models of natural inflation based on closed string axions are incompatible with the weak gravity conjecture (WGC). Specifically, we use T-duality in order to map the bounds on the charge-to-mass ratio of particles imposed by the WGC, to constraints on the ratio between instanton actions and axion decay constants. We use this connection to prove that if the WGC holds, even when multiple axions are present and mix with each other, one cannot have large axion decay constants while remaining in a regime of perturbative control. We also discuss the extension of the WGC to discrete symmetries and its possible impact on models with axion monodromy, and the distinction between the strong and mild versions of the WGC. Finally, we offer some speculations regarding the import of these results to the general theory of inflation.

• The paper provides a rigorous analysis showing quantum gravity enforces sub-Planckian axion decay constants in large field inflation models.
• It applies T-duality to derive bounds linking instanton actions to axion decay constants and extends the Weak Gravity Conjecture to discrete symmetries.
• The work implies many large field inflation models conflict with string theory constraints, guiding future developments in realistic cosmological models.

An Analysis of "Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation"

The paper "Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation," authored by Jon Brown, William Cottrell, Gary Shiu, and Pablo Soler, addresses significant constraints imposed on models of large field inflation within a string-theoretic framework. Specifically, it explores the compatibility of natural inflation models with closed string axions and the Weak Gravity Conjecture (WGC), providing mathematical and theoretical evidence against the feasibility of large axion decay constants within the regime of perturbative control.

Central to this analysis is the application of T-duality to connect the bounds on particle charge-to-mass ratios, as described by the WGC, to constraints on the ratio of instanton actions to axion decay constants. This paper argues that, even in the presence of multiple axions with potential kinetic mixing or alignment, the intrinsic properties of quantum gravity prevent significant expansion of field ranges while maintaining analytic tractability.

The authors extend the WGC to discrete symmetries, considering its ramifications on models of axion monodromy, and delineate between the so-called "strong" and "mild" versions of the WGC. Specifically, the strong version stipulates that the lightest charged particle must respect the conjecture, while the mild version permits the restriction be satisfied by any particle in the spectrum.

Numerically, this rigorous analysis refutes the possibility of large axion decay constants in a controlled regime. It dictates that under the condition of perturbative control, these constants remain sub-Planckian, i.e., not exceeding the Planck mass $M_p$. By leveraging the WGC and T-duality, they offer bounds showing that all decay constants satisfy $f_n \le M_p$.

The broader implications are profound, suggesting that widely explored mechanisms for achieving large field inflation violate the conjecture’s core tenets and are thus unlikely to manifest within credible quantum gravity frameworks like string theory. These findings direct researchers toward a more constrained understanding of inflationary cosmology and stimulate discussions on possible loopholes, such as utilizing axions on torsional cycles to potentially bypass limitations imposed by the WGC.

Beyond inflationary models, the paper explores greater theoretical and philosophical implications regarding the covariance of the WGC under dualities, proposing a generalized conjecture applicable to massive p-form fields. The notion of field space geometry and its interplay with the swampland hypothesis raises questions regarding the realism of many effective field theories claimable from string origins, suggesting that certain ranges of parameters naturally expel themselves from quantum gravity's jurisdiction.

Future perspectives hinted at the research implied a cross-examination of holographic principles, the entropy bound, and their impacts on inflationary paradigms. The tensions observed might illuminate deep insights into the quantum structure of spacetime and the role inflation plays within that ontology. Further investigations might involve exploring the intersection of these quantum gravitational constraints with cosmological predictions and potential observational signatures.

In conclusion, the findings by Brown et al. lay a firm, albeit restrictive, foundation for future inflationary model developments. This work emphasizes string theory's rigors and quantum gravity's principles, ensuring that productive directions toward realistic models are pursued in inflationary cosmology, while those inclined to trans-Planckian dynamics remain critically examined within a broader theoretical context.