An Ignoble Approach to Large Field Inflation

TL;DR

The paper analyzes axion monodromy inflation in which a sub-Planckian axion couples to a topological 4-form to produce an effective quadratic potential $V(\phi)=\tfrac{1}{2}\mu^2\phi^2$, enabling high-scale inflation with potentially detectable tensor modes. It thoroughly assesses quantum corrections within a 4d EFT, deriving constraints that require heavy moduli ($M\gtrsim H$) and controlled light states from multiple windings, while ensuring UV scales $\Lambda$ lie appropriately relative to the inflationary energy. Perturbative inflaton and graviton loops are shown not to spoil slow-roll due to an approximately preserved shift symmetry, and the paper catalogs direct and indirect corrections (including a dual 2-form formulation) arising from UV physics and moduli stabilization. The findings suggest that high-scale inflation in this framework is viable with distinctive observational signatures, such as resonant non-Gaussianity and oscillatory power-spectrum features, contingent on UV completion near the GUT scale and the suppression of problematic corrections.

Abstract

We study an inflationary model developed by Kaloper and Sorbo, in which the inflaton is an axion with a sub-Planckian decay constant, whose potential is generated by mixing with a topological 4-form field strength. This gives a 4d construction of "axion monodromy inflation": the axion winds many times over the course of inflation and draws energy from the 4-form. The classical theory is equivalent to chaotic inflation with a quadratic inflaton potential. Such models can produce "high scale" inflation driven by energy densities of the order of $(10^{16}\ GeV)^4$, which produces primordial gravitational waves potentially accessible to CMB polarization experiments. We analyze the possible corrections to this scenario from the standpoint of 4d effective field theory, identifying the physics which potentially suppresses dangerous corrections to the slow-roll potential. This yields a constraint relation between the axion decay constant, the inflaton mass, and the 4-form charge. We show how these models can evade the fundamental constraints which typically make high-scale inflation difficult to realize. Specifically, the moduli coupling to the axion-four-form sector must have masses higher than the inflationary Hubble scale ($\la\ 10^{14}\ GeV$). There are also constraints from states that become light due to multiple windings of the axion, as happens in explicit string theory constructions of this scenario. Further, such models generally have a quantum-mechanical "tunneling mode" in which the axion jumps between windings, which must be suppressed. Finally, we outline possible observational signatures.

Figures (5)

• Figure 1: A map of the possible energies as a function of $\phi$, for the potential $V = \frac{1}{2}(\mu \phi + q)^2$. The picture repeats itself (except for the labeling of the lines) each time one shifts $\phi \to \phi + |e|/m\equiv \phi + f_{\phi}$.
• Figure 2: The solid red lines are the actual energies of the system as a function of the inflaton in flat space, when the Hamiltonian has matrix elements connecting adjacent values of $q$. The dashed blue lines are the energy eigenstates when these matrix elements vanish.
• Figure 3: A "daisy diagram" that contributes to the one-loop effective potential.
• Figure 4: The effects of a shift of the complex structure $\tau \to \tau + 1$ of a 2-torus, in the presence of a D-brane wrapping a cycle of the torus.
• Figure 5: Light states in the presence of a multiply wrapped D-brane. If the torus is a square with sides of length $L$, and the brane wraps the cycle $A + n B$, the short stretched string shown will have length $L/\sqrt{1+n^2}$. The total length of the wrapped brane is $L \sqrt{1 + n^2}$, so the lowest momentum mode will have mass $1/(L\sqrt{1 + n^2})$.