### Abstract

We propose an extension of natural inflation, where the inflaton potential is a general periodic function. Specifically, we study elliptic inflation where the inflaton potential is given by Jacobi elliptic functions, Jacobi theta functions or the Dedekind eta function, which appear in gauge and Yukawa couplings in the string theories compactified on toroidal backgrounds. We show that in the first two cases the predicted values of the spectral index and the tensor-to-scalar ratio interpolate from natural inflation to exponential inflation such as R^{2}- and Higgs inflation and brane inflation, where the spectral index asymptotes to n_{s} = 1 − 2/N ≃ 0.967 for the e-folding number N = 60. We also show that a model with the Dedekind eta function gives a sizable running of the spectral index due to modulations in the inflaton potential. Such elliptic inflation can be thought of as a specific realization of multi-natural inflation, where the inflaton potential consists of multiple sinusoidal functions. We also discuss examples in string theory where Jacobi theta functions and the Dedekind eta function appear in the inflaton potential.

Original language | English |
---|---|

Journal | Journal of High Energy Physics |

Volume | 2015 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 Mar 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Cosmology of Theories beyond the SM
- Supergravity Models
- Superstring Vacua

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

^{2}-inflation.

*Journal of High Energy Physics*,

*2015*(3). https://doi.org/10.1007/JHEP03(2015)129

**Elliptic inflation : interpolating from natural inflation to R ^{2}-inflation.** / Higaki, Tetsutaro; Takahashi, Fuminobu.

Research output: Contribution to journal › Article

^{2}-inflation',

*Journal of High Energy Physics*, vol. 2015, no. 3. https://doi.org/10.1007/JHEP03(2015)129

^{2}-inflation. Journal of High Energy Physics. 2015 Mar 1;2015(3). https://doi.org/10.1007/JHEP03(2015)129

}

TY - JOUR

T1 - Elliptic inflation

T2 - interpolating from natural inflation to R2-inflation

AU - Higaki, Tetsutaro

AU - Takahashi, Fuminobu

PY - 2015/3/1

Y1 - 2015/3/1

N2 - We propose an extension of natural inflation, where the inflaton potential is a general periodic function. Specifically, we study elliptic inflation where the inflaton potential is given by Jacobi elliptic functions, Jacobi theta functions or the Dedekind eta function, which appear in gauge and Yukawa couplings in the string theories compactified on toroidal backgrounds. We show that in the first two cases the predicted values of the spectral index and the tensor-to-scalar ratio interpolate from natural inflation to exponential inflation such as R2- and Higgs inflation and brane inflation, where the spectral index asymptotes to ns = 1 − 2/N ≃ 0.967 for the e-folding number N = 60. We also show that a model with the Dedekind eta function gives a sizable running of the spectral index due to modulations in the inflaton potential. Such elliptic inflation can be thought of as a specific realization of multi-natural inflation, where the inflaton potential consists of multiple sinusoidal functions. We also discuss examples in string theory where Jacobi theta functions and the Dedekind eta function appear in the inflaton potential.

AB - We propose an extension of natural inflation, where the inflaton potential is a general periodic function. Specifically, we study elliptic inflation where the inflaton potential is given by Jacobi elliptic functions, Jacobi theta functions or the Dedekind eta function, which appear in gauge and Yukawa couplings in the string theories compactified on toroidal backgrounds. We show that in the first two cases the predicted values of the spectral index and the tensor-to-scalar ratio interpolate from natural inflation to exponential inflation such as R2- and Higgs inflation and brane inflation, where the spectral index asymptotes to ns = 1 − 2/N ≃ 0.967 for the e-folding number N = 60. We also show that a model with the Dedekind eta function gives a sizable running of the spectral index due to modulations in the inflaton potential. Such elliptic inflation can be thought of as a specific realization of multi-natural inflation, where the inflaton potential consists of multiple sinusoidal functions. We also discuss examples in string theory where Jacobi theta functions and the Dedekind eta function appear in the inflaton potential.

KW - Cosmology of Theories beyond the SM

KW - Supergravity Models

KW - Superstring Vacua

UR - http://www.scopus.com/inward/record.url?scp=84961376892&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961376892&partnerID=8YFLogxK

U2 - 10.1007/JHEP03(2015)129

DO - 10.1007/JHEP03(2015)129

M3 - Article

AN - SCOPUS:84961376892

VL - 2015

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 3

ER -