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Multi-Natural Inflation in Supergravity and BICEP2

Michael Czerny, Tetsutaro Higaki, Fuminobu Takahashi

TL;DR

The paper investigates multi-natural inflation realized in supergravity, where the inflaton is an axion-like field with a potential that is a sum of sinusoidal terms. It demonstrates that two sinusoidal components can generate a wide range of tensor-to-scalar ratios $r$ and spectral indices $n_s$, including values near or above unity with sizable running, potentially alleviating tensions between BICEP2 and Planck. It develops both one-axion and two-axion constructions, analyzes saxion stabilization, and outlines UV completions inspired by string theory with moduli stabilization. The work highlights that small modulations in the potential are a natural feature of the framework and that future cosmological data on running and neutrino/dark radiation content can further test these scenarios.

Abstract

We revisit the recently proposed multi-natural inflation and its realization in supergravity in light of the BICEP2 results. Multi-natural inflation is a single-field inflation model where the inflaton potential consists of multiple sinusoidal functions, and it is known that a sizable running spectral index can be generated, which relaxes the tension between the BICEP2 and the Planck results. In this paper we show that multi-natural inflation can accommodate a wide range of values of $(n_s, r)$, including the spectral index close to or even above unity. This will be be favored if the tension is resolved by other sources such as dark radiation, hot dark matter, or non-zero neutrino mass. We also discuss the implications for the implementation in string theory.

Multi-Natural Inflation in Supergravity and BICEP2

TL;DR

The paper investigates multi-natural inflation realized in supergravity, where the inflaton is an axion-like field with a potential that is a sum of sinusoidal terms. It demonstrates that two sinusoidal components can generate a wide range of tensor-to-scalar ratios and spectral indices , including values near or above unity with sizable running, potentially alleviating tensions between BICEP2 and Planck. It develops both one-axion and two-axion constructions, analyzes saxion stabilization, and outlines UV completions inspired by string theory with moduli stabilization. The work highlights that small modulations in the potential are a natural feature of the framework and that future cosmological data on running and neutrino/dark radiation content can further test these scenarios.

Abstract

We revisit the recently proposed multi-natural inflation and its realization in supergravity in light of the BICEP2 results. Multi-natural inflation is a single-field inflation model where the inflaton potential consists of multiple sinusoidal functions, and it is known that a sizable running spectral index can be generated, which relaxes the tension between the BICEP2 and the Planck results. In this paper we show that multi-natural inflation can accommodate a wide range of values of , including the spectral index close to or even above unity. This will be be favored if the tension is resolved by other sources such as dark radiation, hot dark matter, or non-zero neutrino mass. We also discuss the implications for the implementation in string theory.

Paper Structure

This paper contains 8 sections, 28 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Multi-natural inflation in supergravity
  3. Setup and saxion stabilization in the case of one axion
  4. Multi-natural inflation with two sinusoidal functions
  5. A case of two axions for a large decay constant
  6. Toward a UV completion
  7. Spectral index and tensor-to-scalar ratio
  8. Discussion and Conclusions

Figures (1)

  • Figure 1: Left: the prediction of $(n_s, r)$ of multi-natural inflation Solid (dashed) lines correspond to $N = 60$ ($N = 50$) e-folds before the end of inflation. Predictions of $(n_s, r)$ for a few values of $f$ are shown on the brown dashed curve. See the text for the explanation of the shaded regions. The allowed region will be shifted to larger values of $n_s$ if the effective neutrino species is varied instead of the running spectral index. Right: the inflaton potential with multiple values for the decay constant $f$. The potential minimum is shifted to the origin for visualization purpose. When calculating the field excursion, we assume $N = 60$ e-folds.