Axion Inflation and Gravity Waves in String Theory

TL;DR

This work assesses whether string theory can produce observable inflationary gravitational waves via axion-based mechanisms, focusing on N-flation and axion valley (natural inflation) scenarios. It systematically analyzes KKLT-like stabilization, α′ corrections, and supergravity constructions, finding that in Calabi–Yau compactifications with logarithmic Kahler potentials, axion inflation in the supergravity regime is hard to realize, while shift-symmetric quadratic Kahler potentials in some limits may permit viable axion inflation with racetrack-type superpotentials. The authors conclude that, within the explored frameworks, working models yielding measurable tensor modes are not yet established, though several promising avenues (e.g., racetrack W, quadratic Kahler potentials, orientifold constructions) warrant further study. The results underscore significant challenges in reconciling moduli stabilization with large axion decay constants and large-field inflation in string theory, shaping the outlook for future CMB probes of $r$ and $n_s$ in testing string-inspired cosmology.

Abstract

The majority of models of inflation in string theory predict an absence of measurable gravitational waves, r << 10^{-3}. The most promising proposals for making string theoretic models that yield measurable tensor fluctuations involve axion fields with slightly broken shift symmetry. We consider such models in detail, with a particular focus on the N-flation scenario and on axion valley/natural inflation models. We find that in Calabi-Yau threefold compactifications with logarithmic Kahler potentials K it appears to be difficult to meet the conditions required for axion inflation in the supergravity regime. However, in supergravities with an (approximately) quadratic shift-symmetric K, axion inflation may be viable. Such Kahler potentials do arise in some string models, in specific limits of the moduli space. We describe the most promising classes of models; more detailed study will be required before one can conclude that working models exist.

Figures (3)

• Figure 1: Axion valley potential (\ref{['full']}), (\ref{['valley']}). On the left there is a view of the axion valley. There is a sharp minimum for $x$ and a very shallow minimum for $\beta$. The $\beta$-direction is practically flat for $\beta$ from $0$ to $20$ (in Planck units), whereas in the $x$-direction the potential appreciates significantly when $x$ changes by $0.1$. On the right, the potential is plotted for $\beta$ from $0$ to 300. The plot shows the periodicity in the axion variable $\beta$. Both $\beta$ and $x$ have canonical kinetic terms.
• Figure 2: The funnel-type potential of the KKLT model with logarithmic shift symmetric Kähler potential depending on the volume $\sigma$ and the axion $\alpha$. The potential in the axion direction is as steep as in the volume modulus direction.
• Figure 3: Volume-axion slices of the double valley potential (\ref{['U']}). On the left the volume slice of the potential is plotted at the minimum for the axion at $\beta={100\pi\over 3}$. The plot shows two minima and a maximum in between. On the right there is a slice of the axion periodic potential with the period ${2\pi\over a-b}$ at the minimum of the volume, $x= 3.21$ in our example, with $(a-b)=3/100$. There is a maximum at $\beta= 2n{100\pi\over 3}$ and a minimum at $\beta= (2n+1){100\pi\over 3}$, $n=0,1, 2, ...$.