Robust Inflation from Fibrous Strings

TL;DR

The paper argues that robust, UV-complete inflation can arise from exponential-type potentials sourced by fibred string compactifications within the Large Volume Scenario. It shows that a fibre modulus can act as the inflaton, producing a plateau-like potential with an exponential tail that yields a predictable relation between the tensor-to-scalar ratio and the spectral index, $r \\propto (n_s - 1)^2$, typically with $r \lesssim 0.01$. The robustness is analyzed against string-loop and higher-curvature corrections, with extended no-scale structure and the generic prevalence of fibration in Calabi-Yau manifolds supporting stability of predictions. The framework connects low-energy observables to the high-energy UV completion, constraining large-field inflation and guiding future tests of tensor modes while highlighting the tension between large-field inflation and low-energy supersymmetry. Overall, the Fibre Inflation class provides a predictive, UV-mound inflationary scenario with clear observational signatures and tight theoretical constraints.

Abstract

Successful inflationary models should (i) describe the data well; (ii) arise generically from sensible UV completions; (iii) be insensitive to detailed fine-tunings of parameters and (iv) make interesting new predictions. We argue that a class of models with these properties is characterized by relatively simple potentials with a constant term and negative exponentials. We here continue earlier work exploring UV completions for these models, including the key (though often ignored) issue of modulus stabilisation, to assess the robustness of their predictions. We show that string models where the inflaton is a fibration modulus seem to be robust due to an effective rescaling symmetry, and fairly generic since most known Calabi-Yau manifolds are fibrations. This class of models is characterized by a generic relation between the tensor-to-scalar ratio $r$ and the spectral index $n_s$ of the form $r \propto (n_s -1)^2$ where the proportionality constant depends on the nature of the effects used to develop the inflationary potential and the topology of the internal space. In particular we find that the largest values of the tensor-to-scalar ratio that can be obtained by generalizing the original set-up are of order $r \lesssim 0.01$. We contrast this general picture with specific popular models, such as the Starobinsky scenario and $α$-attractors. Finally, we argue the self consistency of large-field inflationary models can strongly constrain non-supersymmetric inflationary mechanisms.

Figures (3)

• Figure 1: $V$ versus $\hat{\phi}$ for $k=2/\sqrt{3}$ and $R=2.25\cdot 10^{-5}$.
• Figure 2: $\epsilon$ and $\eta$ versus $\hat{\phi}$ for $k=2/\sqrt{3}$ and $R=2.25\cdot 10^{-5}$.
• Figure 3: Fibre inflation fits in the $\alpha$ attractors class of models corresponding to $\alpha=2$ and can be seen as a stringy realisation of $\alpha$ attractors (figure adapted from ckl). Other string scenarios such as Kähler moduli inflation and Poly-instanton inflation are also in this class but with much smaller values of $r$ and then unobservable tensor modes.