Accidental Inflation in String Theory

TL;DR

This work demonstrates that inflation driven by the volume modulus can occur in type IIB string theory using the KL racetrack stabilization, with two AdS minima uplifted to a dS vacuum and inflation arising near a flat saddle or inflection point. The model yields a long slow-roll epoch (roughly 193 e-folds in the presented example) and a COBE-normalized amplitude $\Delta_{\mathcal{R}}^2 \approx 2.9\times10^{-9}$, while predicting a small tensor fraction $r<10^{-6}$ and a spectral index in the range $n_s \approx 0.93$–$0.95$. The authors argue that the required fine-tuning of the potential is natural in the string landscape due to volume-weighted measures that favor extended slow-roll inflation. They show that if the potential near the critical point is cubic (or quartic with $Z_2$ symmetry), the asymptotic $n_s$ values are $\approx 0.93$ (no $Z_2$) or $\approx 0.95$ (with $Z_2$), respectively, offering a tentative, testable signature for this class of inflationary scenarios. Eternal inflation and diffusion considerations further support these predictions under plausible measure choices.

Abstract

We show that inflation in type IIB string theory driven by the volume modulus can be realized in the context of the racetrack-based Kallosh-Linde model (KL) of moduli stabilization. Inflation here arises through the volume modulus slow-rolling down from a flat hill-top or inflection point of the scalar potential. This situation can be quite generic in the landscape, where by uplifting one of the two adjacent minima one can turn the barrier either to a flat saddle point or to an inflection point supporting eternal inflation. The resulting spectral index is tunable in the range of 0.93 < n_s < 1, and there is only negligible production of primordial gravitational waves r < 10^{-6}. The flatness of the potential in this scenario requires fine-tuning, which may be justified taking into account the exponential reward by volume factors preferring the regions of the universe with the maximal amount of slow-roll inflation. This consideration leads to a tentative prediction of the spectral index $n_s\approx 0.95$ or $n_s \approx 0.93$ depending on whether the potential has a symmetry phi -> - phi or not.

Figures (6)

• Figure 1: The thick blue solid line shows the inflationary potential for the model of Ref. Holman:1984yj, with $\Phi_{0} = 1$. If one takes the model with a slightly larger $\Phi_{0}$, the potential has two minima separated by a barrier, as shown by the thin green dashed line, corresponding to $\Phi_{0} = 1.05$. For $\Phi_{0}<1$, the metastable minimum disappears, and $V'$ becomes negative everywhere, as shown by the thin red solid line corresponding to $\Phi_{0} = 0.95$. Inflation is possible only if $|\Phi_{0}-1|\ll 1$, which requires fine tuning.
• Figure 2: The uplifted potential for $W_0= 4\cdot 10^{-8},\ A=1,\ B=-0.62704017319,\ a=2\pi/58, b=2\pi/60,\ C=3.01\cdot 10^{-18}$. The potential is shown in units of $10^{{-23}}$ of the Planck density. A late-time dS minimum at $V\approx 0$ stabilizes the volume at $\varphi_{\rm dS}\approx 157.1$. A tunable dS saddle or inflection point, which is responsible for inflation, is at $\varphi_{cr}\approx 144.5$. There is a barrier at $\varphi \sim 200$ protecting the late-time dS minimum. The height of the barrier exceeds the height of the inflationary saddle/inflection point implying an absence of the cosmological overshoot problem Brustein:1992nkkaloper.
• Figure 3: The potential as a function of the complex field $T = \varphi +i\tau$, in units of $10^{{-23}}$ of the Planck density. The inflationary saddle/inflection point and the late-time dS minimum both occur at $\tau = {\rm Im}~T =0$, as shown in the analytic investigation.
• Figure 4: The evolution of the volume modulus $t$ as a function of the total number of e-folds $N$.
• Figure 5: The spectral index of the density fluctuations as a function of the total number of e-folds $N$. The blue arrow denotes the spectral index at the time when the COBE normalization scale left the horizon, i.e. at $N_e^{\rm CMB}=60$ e-folds before the end of inflation.