Fibre Inflation: Observable Gravity Waves from IIB String Compactifications

TL;DR

Fibre Inflation embeds a large-field inflationary scenario within Type IIB string theory’s LARGE Volume Framework, leveraging a K3-fiber modulus whose potential is lifted by string-loop corrections. The inflaton dynamics are dominated by the fiber modulus, with the overall volume fixed by leading ${\alpha'}$ and nonperturbative effects, yielding a flat direction lifted by loops that yields an approximately exponential potential in a canonically normalised field. The model predicts a robust relation between the tensor-to-scalar ratio and the scalar spectral index, $r \simeq 6(n_s-1)^2$, and can produce $n_s\approx 0.97$ with $r$ around a few \(\times 10^{-3}\) to \(10^{-2}\) for plausible reheating histories; in two-field analyses the results remain compatible with observations and COBE normalisation, while avoiding the typical $\eta$-problem via the LVS no-scale structure. Overall, Fibre Inflation offers a natural, string-theoretic route to observable primordial gravity waves with predictions that are robust across a class of LVS compactifications and Calabi–Yau geometries, motivating further explicit constructions and reheating studies.

Abstract

We introduce a simple string model of inflation, in which the inflaton field can take trans-Planckian values while driving a period of slow-roll inflation. This leads naturally to a realisation of large field inflation, inasmuch as the inflationary epoch is well described by the single-field scalar potential $V = V_0 (3-4 e^{-\hat\varphi/\sqrt{3}})$. Remarkably, for a broad class of vacua all adjustable parameters enter only through the overall coefficient $V_0$, and in particular do not enter into the slow-roll parameters. Consequently these are determined purely by the number of \e-foldings, $N_e$, and so are not independent: $\varepsilon \simeq \frac32 η^2$. This implies similar relations among observables like the primordial scalar-to-tensor amplitude, $r$, and the scalar spectral tilt, $n_s$: $r \simeq 6(n_s - 1)^2$. $N_e$ is itself more model-dependent since it depends partly on the post-inflationary reheat history. In a simple reheating scenario a reheating temperature of $T_{rh}\simeq 10^{9}$ GeV gives $N_e\simeq 58$, corresponding to $n_s\simeq 0.970$ and $r\simeq 0.005$, within reach of future observations. The model is an example of a class that arises naturally in the context of type IIB string compactifications with large-volume moduli stabilisation, and takes advantage of the generic existence there of Kahler moduli whose dominant appearance in the scalar potential arises from string loop corrections to the Kahler potential. The inflaton field is a combination of Kahler moduli of a K3-fibered Calabi-Yau manifold. We believe there are likely to be a great number of models in this class -- `high-fibre models' -- in which the inflaton starts off far enough up the fibre to produce observably large primordial gravity waves.

Figures (15)

• Figure 1: $V$ (arbitrary units) versus $\tau_1$ and $\tau_3$ for one of the parameter sets discussed in the text, with $\mathcal{V}$ evaluated at its minimum.
• Figure 2: $V$ (in arbitrary units) versus $\hat{\varphi}$, with $\mathcal{V}$ and $\tau_{3}$ fixed at their minima. The plot assumes the parameters used in the text (for which $\hat{\varphi}_{ip} \simeq 0.80$, $\hat{\varphi}_{end} = 1.0$, and $R\equiv\mathcal{C}_0/\mathcal{C}_2\sim 10^{-6}$).
• Figure 3: Plots of the potential and the slow-roll parameters $\varepsilon$ and $\eta$ vs $\hat{\varphi}$ for $R=10^{-8}$ (blue curve), $R=10^{-6}$ (green curve), and $R=10^{-4}$ (red curve).
• Figure 4: Plot of the number of $e$-foldings, $N_e$, vs $\hat{\varphi}_*$ (left) and $\hat{\varphi}_{end}$ (right) for $R=0$. The inflection point occurs at $\hat{\varphi}_{ip} \simeq 0.8$ and $\hat{\varphi}_{end} = 1$ in the left-hand plot. $\hat{\varphi}_* = 5.7$ in the right-hand plot. The solid (red) curves are computed using the full potential (3.33) while the dashed (blue) curves are computed using the approximate potential (3.38).
• Figure 5: Plot of the maximum number of $e$-foldings, $N_e^{max}$, vs $x=\log_{10}R$, defined by the condition $\hat{\varphi}_* = \hat{\varphi}_0(R)$ as described in the text. The integration takes $\hat{\varphi}_{end} = 1$, and the curves are computed using the approximate potential (3.38).