On Inflation in String Theory

TL;DR

The work surveys how inflation can be realized within string theory, emphasizing flux compactification and moduli stabilization as a framework for viable models. It covers string-inspired supergravity realizations (including chaotic and axion-valley inflation), brane-inflation scenarios in warped geometries, and modular inflation with racetrack and large-volume constructions, highlighting their observational predictions such as $n_s$ around $0.95$ and typically small $r$. The analysis discusses conceptual and technical challenges, including the eta problem, moduli stabilization, and the need for explicit string derivations to yield falsifiable predictions. Overall, the paper argues that cosmological data could, in principle, test string-theory inflationary frameworks, provided robust string constructions with distinctive observables can be established.

Abstract

In this talk we describe recent progress in construction of inflationary models in the context of string theory with flux compactification and moduli stabilization. We also discuss a possibility to test string theory by cosmological observations.

Figures (8)

• Figure 1: KKLT potential as a function of the volume of extra dimensions $\sigma= {T+\bar{T}\over 2}$.
• Figure 2: The funnel-type potential of the KKLT model depending on the volume $\sigma$ and the axion $\alpha$ from Kallosh:2004rs. Fig. 1 in Sec. 2 of this paper gives a slice of this potential in $\sigma$ direction at the minimum for the axion. The potential in the axion direction is as steep as in the volume modulus direction.
• Figure 3: Axion valley potential (\ref{['full']}), (\ref{['valley']}). On the left figure there is a view on 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 figure, 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 4: A plot for the racetrack potential (rescaled by $10^{16}$). Inflation begins in a vicinity of any of the saddle points. Units are $M_p=1$. As one can see, the potential is periodic in the axion direction, but it is very much different from the potential of natural inflation: there is no axion valley here.
• Figure 5: Plot for a racetrack type potential (rescaled by $10^{16}$). Inflation begins in a vicinity of the saddle point and ends up in one of the two minima, depending on initial conditions. Note that near the minima the potential has a KKLT type funnel shape where the curvature in volume and axion direction is of the same scale for canonical variables $X/X_{min}$ and $Y/X_{min}$.