**Authors:**

(1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp);

(2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp).

## Table of Links

2 U(1) gauge theory on a warped background

3 Gauge-Higgs inflation on a warped background

4 Conclusions and discussions, Acknowledgements, and References

## Abstract

We investigate whether inflation in the early universe can be induced by an extra component of a five-dimensional U(1) gauge field in the Randall-Sundrum warped spacetime or not. We show that an effective potential obtained by quantum corrections can act as an inflaton potential by finding parameter regions consistent with Planck 2018 results. In our model, fields involved in inflation obey a different type of boundary condition from that of the visible particles, and a surviving Wilson line phase can play a specific role for physics beyond the standard model.

## 1 Introduction

Inflation can solve both the flatness problem and the horizon problem at the same time and also explain temperature fluctuations of the cosmic microwave background (CMB) [1]. It is therefore almost certain that inflation occurred in the early universe. However, a specific mechanism or an origin of a quanta called “inflaton” is still a mystery.

An inflaton is assumed to be a scalar field in typical models, but its potential is, in general, not stable against quantum (gravity) corrections and should be fine-tuned to satisfy constraints of cosmological observations. This problem stems from the fact that radiative corrections on scalar fields cannot be controlled without any assistance of a powerful symmetry.

One way to solve this problem is to consider a higher-dimensional gauge theory, and then a Wilson line phase made of an extra component of a gauge field can become an inflaton whose potential can be determined by the gauge principle. In this scenario, a relevant part of potential is obtained as a function of the Wilson line phase radiatively, taking a finite value [2, 3]. Such an inflaton potential is robust owing to the gauge symmetry and its stability can be guaranteed. A famous five-dimensional (5d) model compactified on a circle S 1 has been proposed in the name of extranatural inflation [4]. In a similar setup, a model with both a radion and a Wilson line phase has been constructed, and it is shown that the radion is stabilized [5] and the Wilson line phase can be, in most cases, an inflaton [6].

Recently, constraints on cosmological parameters from various observations have become more stringent and inflation models can be selected more rigorously [7]. It is valuable to reexamine whether an extranatural inflation scenario is still valid today or not, in a wide variety of spacetime. It is known that the Randall-Sundrum (RS) warped spacetime can provide rich properties in phenomenological aspects of particle physics. For instance, RS1 model provides a solution of the hierarchy problem of the standard model [8], RS2 model explains the weakness of gravitational force on the TeV brane because the graviton localizes on the Planck brane [9], and gauge-Higgs unification (GHU) models in the warped spacetime can show promise as physics beyond the standard model (BSM) [10, 11, 12, 13]. Hence, it would be favorable if a riddle in cosmology such as inflation could be solved in the same background.

In this paper, we investigate whether inflation in the early universe can be induced by an extra component of a 5d U(1) gauge field in the warped background or not. In concrete, we examine whether an effective potential obtained by quantum corrections can act as an inflaton potential by finding parameter regions consistent with Planck 2018 results or not. The RS spacetime contains an orbifold S 1/Z2 and a different type of boundary condition called “conjugate boundary condition” can be imposed on fields to survive an extra component of a gauge boson in QED-like models and this enables fields involved in inflation to play a specific role for BSM.

This paper is organized as follows. In the next section, we present a 5d U(1) gauge theory on the warped spacetime. In section 3, we study an extranatural inflation scenario on the warped spacetime based on our model. The last section is devoted to conclusions and discussions.

This paper is available on arxiv under CC BY 4.0 DEED license.