Transplanckian Censorship and Global Cosmic Strings

TL;DR

This work investigates whether transplanckian axion excursions in large-field inflation can be accessed by external observers, using supercritical global cosmic strings as a controlled laboratory. It analyzes two toy EFT realizations—a 4D $\Phi^4$ axion model and a 5D Wilson-loop axion model—finding that string cores inflate topologically when $n f \gtrsim M_p$, with exponential inflation in the 4D case and power-law inflation in the Wilson-loop case. The exterior spacetime is shown to be a nonsingular cigar geometry, arising from radion dynamics driven by axion flux, and causal analysis reveals that circumnavigation requires exponentially long times, while topological censorship constrains loops from revealing the full excursion. Collectively, the results establish a concrete gravitational context in which transplanckian excursions are effectively censored and point to future studies of loop dynamics, quantum effects, and broader UV completions of axion monodromy via Wilson-loop or other compactifications.

Abstract

Large field excursions are required in a number of axion models of inflation. These models also possess global cosmic strings, around which the axion follows a path mirroring the inflationary trajectory. Cosmic strings are thus an interesting theoretical laboratory for the study of transplanckian field excursions. We describe connections between various effective field theory models of axion monodromy and study the classical spacetimes around their supercritical cosmic strings. For small decay constants $f<M_p$ and large winding numbers $n>M_p/f$, the EFT is under control and the string cores undergo topological inflation, which may be either of exponential or power-law type. We show that the exterior spacetime is nonsingular and equivalent to a decompactifying cigar geometry, with the radion rolling in a potential generated by axion flux. Signals are able to circumnavigate infinite straight strings in finite but exponentially long time, $t\sim e^{Δa/M_p}$. For finite loops of supercritical string in asymptotically flat space, we argue that if topological inflation occurs, then topological censorship implies transplanckian censorship, or that external observers are forbidden from threading the loop and observing the full excursion of the axion.

Figures (7)

• Figure 1: Left: The proper radius of the locus $\phi=0.1f$ as a function of time for $n=10,30,40$ (from bottom to top) and $\epsilon=1/100$. For $n=40$ the core inflates. Right: The Kretschmann scalar curvature. Time starts at $0$ with the top curve, corresponding to a flat initial-value metric, and increases for each line below that, saturating at a substantially subplanckian value of order $\epsilon^4$ in the core.
• Figure 2: The evolution of the axial metric exponent $B(t,r)$ on a number of fixed time-slices for subcritical $n=10$ (left) and supercritical $n=40$ (right) strings with $\epsilon=1/100$. Time starts at $0$ with the bottom curve, corresponding to a flat initial-value metric, and increases for each line above that. In both scenarios, $g_{zz}$ grows exponentially with $t$, while the coordinate boundary of the core contracts exponentially with $t$.
• Figure 3: Schematic form of a stabilized radion potential.
• Figure 4: Numerical analysis of a cosmic string in a sample 5D model with $g=1,~n=16,~v_r^2M_p^2=1/2,$ and radion potential $V=\frac{2}{R^6}-\frac{5}{R^3}+\frac{3}{R}$, in units where the Minkowski vacuum is at $v_R=1$. Left: Equally-spaced timeslices of the radial profile of the radion field (time runs bottom to top). A domain wall forms around $r\simeq 38$, outside of which $R$ takes its vacuum value. Right: Time dependence of the proper distance between $r=0$ and $r=37$ (purple dots), with a fit to a model of the form $c_1 (c_2+t)^3$ (green line).
• Figure 5: Late-time behavior of $g_{\theta\theta}(t,r)$ exterior to the string core in $\Phi^4$ theory with $n=20,~\epsilon=1/10$. Lines represent equally-spaced $t$-slices of the numerical solution, advancing bottom to top.