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Coupling Hybrid Inflation to Moduli

Ph. Brax, C. van de Bruck, A. C. Davis, Stephen C. Davis

TL;DR

This work analyzes F-term hybrid inflation in a supergravity framework that includes a moduli sector, revealing that moduli couplings introduce a tree-level slope and mass for the inflaton and that loop corrections add further curvature. Moduli dynamics during inflation generate a significant backreaction, typically yielding a large negative eta (often around η ≈ −6) and compromising slow-roll unless shift symmetries in the inflaton sector and a no-scale moduli sector are implemented. In KKLT-like moduli stabilisation scenarios, these backreactions persist, and viable slow-roll inflation generally requires substantial fine-tuning of the moduli superpotential. The findings emphasize that moduli backreaction cannot be neglected in string-inspired inflation models and that achieving consistent slow-roll inflation in this framework remains challenging without carefully engineered symmetries or lifting terms.

Abstract

Hybrid inflation can be realised in low-energy effective string theory, as described using supergravity. We find that the coupling of moduli to F-term hybrid inflation in supergravity leads to a slope and a curvature for the inflaton potential. The epsilon and eta parameters receive contributions at tree and one loop level which are not compatible with slow roll inflation. Furthermore the coupling to the moduli sector can even prevent inflation from ending at all. We show that introducing shift symmetries in the inflationary sector and taking the moduli sector to be no-scale removes most of these problems. If the moduli fields are fixed during inflation, as is usually assumed, it appears that viable slow-roll inflation can then be obtained with just one fine-tuning of the moduli sector parameters. However, we show this is not a reasonable assumption, and that the small variation of the moduli fields during inflation gives a significant contribution to the effective inflaton potential. This typically implies that eta is approximately -6, although it may be possible to obtain smaller values with heavy fine-tuning.

Coupling Hybrid Inflation to Moduli

TL;DR

This work analyzes F-term hybrid inflation in a supergravity framework that includes a moduli sector, revealing that moduli couplings introduce a tree-level slope and mass for the inflaton and that loop corrections add further curvature. Moduli dynamics during inflation generate a significant backreaction, typically yielding a large negative eta (often around η ≈ −6) and compromising slow-roll unless shift symmetries in the inflaton sector and a no-scale moduli sector are implemented. In KKLT-like moduli stabilisation scenarios, these backreactions persist, and viable slow-roll inflation generally requires substantial fine-tuning of the moduli superpotential. The findings emphasize that moduli backreaction cannot be neglected in string-inspired inflation models and that achieving consistent slow-roll inflation in this framework remains challenging without carefully engineered symmetries or lifting terms.

Abstract

Hybrid inflation can be realised in low-energy effective string theory, as described using supergravity. We find that the coupling of moduli to F-term hybrid inflation in supergravity leads to a slope and a curvature for the inflaton potential. The epsilon and eta parameters receive contributions at tree and one loop level which are not compatible with slow roll inflation. Furthermore the coupling to the moduli sector can even prevent inflation from ending at all. We show that introducing shift symmetries in the inflationary sector and taking the moduli sector to be no-scale removes most of these problems. If the moduli fields are fixed during inflation, as is usually assumed, it appears that viable slow-roll inflation can then be obtained with just one fine-tuning of the moduli sector parameters. However, we show this is not a reasonable assumption, and that the small variation of the moduli fields during inflation gives a significant contribution to the effective inflaton potential. This typically implies that eta is approximately -6, although it may be possible to obtain smaller values with heavy fine-tuning.

Paper Structure

This paper contains 15 sections, 95 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Combining hybrid inflation with moduli fields
  3. Supergravity P-term inflation
  4. Combined tree-level potential
  5. Inflation
  6. Loop corrections
  7. Moduli fields during $F$-term hybrid inflation
  8. Slow-roll inflation constraints
  9. Moduli destabilisation and the gravitino mass
  10. KKLT scenario
  11. Simple KKLT superpotential
  12. Racetrack superpotential
  13. Analytic arguments
  14. Supersymmetry Breaking Minkowski vacuum
  15. Conclusions

Figures (1)

  • Figure 1: Constraints on the parameters $M^2$ and $\tilde{V}_0$ coming from the observed amplitude of the spectrum (\ref{['norm']}) and the observed spectral index $n_s$ (\ref{['nsconstr']}). The allowed region is the grey area and the values are given in Planck units. It is assumed that $M^2$ is negative, as predicted in these theories.