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 Tduality 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. We argue that, if the strong version is violated, the constraints on large field inflation can be evaded while still satisfying the mild one. Finally, we offer some speculations regarding the import of these results to the general theory of inflation.

AdS-phobia, the WGC, the Standard Model and Supersymmetry

“…From the figures we can safely say that, in these units, the potential takes values from n = 10 to n = 70 in all the cases we have studied (see figures 1-5), so we can take it to be n ∼ 100 to be safe. After plugging in the numbers, one obtains that taking Minkowski as the 3D background metric in the one-loop quantum effective action calculation is justified as long as R −1 10 7 GeV, (C. 6) as in all our models.…”

Can gravitational instantons really constrain axion inflation?

“…10 For the normalisation we found it useful to translate the conventions in [94,95] to our situation.…”

Tunneling in axion monodromy

“…It was furthermore established in [4][5][6] that scenarios involving multiple axions such as N-flation [7] and alignment [8] would fail to suppress higher instanton corrections assuming instantons which contribute dominantly to the inflationary potential satisfy the WGC. Despite the existence of loopholes, these results create substantial obstacles for many models of axionic inflation and may explain why the thorough investigations of [9,10] have not succeeded in finding a large field model which violates WGC motivated bounds.…”

“…In the recent literature [5,14,[16][17][18][19] this tunneling rate has been estimated using results derived by Coleman (and de Luccia in the case of a gravitational theory) [20,21]. However, there are reasons to doubt the validity of these results when applied to axion monodromy.…”

“…This tunneling rate was estimated in [5,14,[17][18][19] using formulas derived in field theory by Coleman [20] and in a gravitational theory by Coleman and de Luccia (CdL) [21].…”