Can Gravitational Instantons Really Constrain Axion Inflation?

TL;DR

The paper investigates whether gravitational instantons—notably Giddings–Strominger wormholes and related dilaton-coupled configurations—can impose robust, model-independent constraints on large-field axion inflation. Using a 4D Einstein–axion (and dilaton) EFT, it derives the spectrum of instanton solutions (wormholes, extremal, and cored) and computes the resulting instanton actions and induced axion potentials, finding that the strongest contributions are generically highly suppressed once a UV cutoff tied to string compactifications is enforced. It further connects these results to moduli stabilization, dilaton couplings arising in string theory, and the Weak Gravity Conjecture, concluding that semiclassical gravitational instantons do not rule out large-field inflation in a broad, model-independent way, though the exact impact can be model-dependent via the dilaton coupling and UV completion. The work highlights the need to understand the ultraviolet spectrum of instantons in quantum gravity to make definitive statements about inflationary constraints. Overall, gravitational instantons provide a fundamental but typically subleading constraint, shifting the search for inflationary bounds to deeper UV physics and non-perturbative string effects.

Abstract

Axions play a central role in inflationary model building and other cosmological applications. This is mainly due to their flat potential, which is protected by a global shift symmetry. However, quantum gravity is known to break global symmetries, the crucial effect in the present context being gravitational instantons or Giddings-Strominger wormholes. We attempt to quantify, as model-independently as possible, how large a scalar potential is induced by this general quantum gravity effect. We pay particular attention to the crucial issue which solutions can or cannot be trusted in the presence of a moduli-stabilisation and a Kaluza-Klein scale. An important conclusion is that, due to specific numerical prefactors, the effect is surprisingly small even in UV-completions with the highest possible scale offered by string theory. As we go along, we discuss in detail Euclidean wormholes, cored and extremal instantons, and how the latter arise from 5d Reissner-Nordstrom black holes. We attempt to dispel possible doubts that wormholes contribute to the scalar potential by an explicit calculation. We analyse the role of stabilised dilaton-like moduli. Finally, we argue that Euclidean wormholes may be the objects satisfying the Weak Gravity Conjecture extended to instantons.

Figures (9)

• Figure 1: Hierarchy of scales in a string model of inflation.
• Figure 2: This picture illustrates a Euclidean wormhole, whose two ends are connected to the same asymptotically flat space. Then there is a non-trivial 1-cycle (dotted line) passing through the wormhole. The cycle orthogonal to this 1-cycle is a $S^3$ (symbolised by the dashed line around the right-hand throat).
• Figure 3: The three types of gravitational instantons are depicted. (a) Euclidean wormhole connecting two asymptotically flat spaces. It is also possible to connect both ends to the same space as shown in \ref{['Figure: Wormhole and 1-Cycle']}. (b) Extremal gravitational instanton: in this case space is flat everywhere. The cross in the middle indicates the locus $r=0$. (c) Cored gravitational instanton: there is a curvature singularity at $r=0$.
• Figure 5: This plot shows dilaton profiles for the cored gravitational instanton with $\alpha = 15$ (solid line) and $\alpha=0.1$ (dashed line). Again, $r$ and $\varphi$ are given in Planck units. For the purpose of illustration we have chosen $K_+ =0.5$ and $n/f_{\text{ax}}$ such that $C/\sinh^2 K_+=1$.
• Figure 6: This picture presents a wormhole which opens at some initial time $t_i$ and closes at $t_f>t_i$. The dotted line indicates the separation of the two events.