Fibre Inflation: Observable Gravity Waves from IIB String Compactifications (0808.0691v3)

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: $\varepsilon \simeq \frac32 \eta^2$. 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.

• The paper introduces a Fibre Inflation model within type IIB compactifications that predicts observable gravity waves with a tensor-to-scalar ratio r ≈ 0.005 and spectral tilt nₛ ≈ 0.970.
• The methodology leverages string loop corrections and Kähler moduli dynamics in a K3-fibered Calabi-Yau framework to achieve robust slow-roll inflation.
• The model’s predictive power emerges from its near parameter-independence, relying primarily on the number of e-foldings to fix inflationary observables.

Overview of "Fibre Inflation: Observable Gravity Waves from IIB String Compactifications"

The paper "Fibre Inflation: Observable Gravity Waves from IIB String Compactifications" by Cicoli, Burgess, and Quevedo, explores the detailed dynamics of a string-theoretic model of cosmological inflation within type IIB string compactifications. It introduces a model wherein the inflaton traverses trans-Planckian field values, achieving a phase of slow-roll inflation with distinctive observable signatures, particularly in the form of primordial gravity waves.

Model Structure and Dynamics

The authors construct a simplified inflationary model leveraging the framework of the Large Volume Scenario (LVS) within type IIB compactifications. The main kinetic activity is driven by Kähler moduli fields within a Calabi-Yau space, specifically a K3-fibered compactification, which naturally leads to what the authors term as 'Fibre Inflation'. The inflaton in this setup is an amalgamation of Kähler moduli whose effective potential is predominantly influenced by string loop corrections.

A remarkable feature of this model is that inflation emerges within the single-field scalar potential space, characterized by:

$$V = V_0 \left( 3 - 4 e^{-\hat\varphi/\sqrt{3}} \right)$$

Here, $V_0$ serves as an overall scaling factor, encapsulating all adjustable parameters, while slow-roll dynamics are fixed by the number of e-foldings $N_e$. A significant outcome is the derived relationship among observables, namely the scalar-to-tensor ratio and the spectral index, given by $r \simeq 6(n_s - 1)^2$.

Major Findings and Implications

1. Inflationary Predictions: The model makes precise predictions for observable inflationary parameters, placing the scalar spectral tilt at $n_s \simeq 0.970$ and the tensor-to-scalar ratio $r \simeq 0.005$ for reasonable reheating temperatures around $T_{rh} \simeq 10^9$ GeV. These parameter values suggest the model is sensitive to future gravitational wave detections in cosmological observations.
2. Parameter Independence of Slow-Roll: Due to the model's structure, the slow-roll parameters are nearly independent of unknown model parameters, depending almost solely on $N_e$, the number of e-foldings between the horizon exit and the end of inflation. This robustness offers a degree of predictive confidence relative to more parameter-sensitive frameworks.
3. Theoretical and Phenomenological Significance: The work pushes the boundaries of incorporating string-theory-motivated constructs in cosmology, providing a theoretically enriched playground for investigating phenomenological potentials with string corrections.
4. New Insights into Kähler Moduli Dynamics: By exploiting the finer properties of logarithmically-flat potentials arising from the K3 fibration structure due to loop corrections, the authors illuminate paths for realizing low-energy, large-field inflation in a natural manner.

Speculations on Future Developments

The methodology paves the way for exploring other Kähler moduli configurations potentially leading to similar inflationary dynamics. Given the unique large-field explorations, similar 'high fibre' models could be investigated considering different Calabi-Yau manifolds or compactifications with higher moduli dimensions, aiming to further bridge string theory with observable cosmology.

Moreover, the incorporation of non-Gaussianity or alternative mechanisms for seed perturbations in these global setups remains an intriguing domain. Ongoing and upcoming observational missions focusing on CMB polarization will be critical in potentially validating these exceptionally structured scenaria.

The integration of constraints and invariances from these string-theoretic solutions offers a fertile ground for granular insights into inflationary periods and their consequences in post-inflationary cosmology, contributing richly to the understanding of the early universe.