Gauss–Bonnet Inflation and the String Swampland

Zhu Yi,Yungui Gong

doi:10.3390/universe5090200

Abstract

The swampland criteria are generically in tension with single-field slow-roll inflation because the first swampland criterion requires small tensor-to-scalar ratio while the second swampland criterion requires either large tensor-to-scalar ratio or large scalar spectral tilt. The challenge to single-field slow-roll inflation imposed by the swampland criteria can be avoided by modifying the relationship between the tensor-to-scalar ratio and the slow-roll parameter. We show that the Gauss–Bonnet inflation with the coupling function inversely proportional to the potential overcomes the challenge by adding a constant factor in the relationship between the tensor-to-scalar ratio and the slow-roll parameter. For the Gauss–Bonnet inflation, while the swampland criteria are satisfied, the slow-roll conditions are also fulfilled, so the scalar spectral tilt and the tensor-to-scalar ratio are consistent with the observations. We use the potentials for chaotic inflation and the E-model as examples to show that the models pass all the constraints. The Gauss–Bonnet coupling seems a way out of the swampland issue for single-field inflationary models.

Highlights

As pointed out in Reference [14], a viable way to solve this problem is by using models with the tensor-to-scalar ratio r reduced by a factor while keeping the lower bound on the field excursion ∆φ as required by the Lyth bound [15], such as warm inflation [16]
With the help of the Gauss–Bonnet coupling, for any potential, the tensor-to-scalar r is reduced by a factor of (1 − λ)2 with the order one parameter λ, so it may solve the swampland problem
The two swampland criteria pose a threat on single-field slow-roll inflation

Summary

Introduction

Inflation solves the flatness and horizon problems in standard cosmology [1,2,3,4,5], and is usually modeled by a single slow-roll scalar field which is obtained from low-energy effective field theories. Condition (2) violates the slow-roll condition and poses a threat to inflationary models by requiring a large tensor-to-scalar ratio r ∼ 8c2. As pointed out in Reference [14], a viable way to solve this problem is by using models with the tensor-to-scalar ratio r reduced by a factor while keeping the lower bound on the field excursion ∆φ as required by the Lyth bound [15], such as warm inflation [16]. With the help of the Gauss–Bonnet coupling, for any potential, the tensor-to-scalar r is reduced by a factor of (1 − λ) with the order one parameter λ, so it may solve the swampland problem. We show that with the help of the Gauss–Bonnet coupling, some inflationary models satisfy the swampland criteria and the observational constraints.

The Gauss–Bonnet Inflation

The Models

The Power-Law Potential

The E-Model

Conclusions