Minimal fine tuning in supersymmetric Higgs inflation

Takumi Imai ,Ken–Iti Izawa

doi:10.1093/ptep/ptu054

Abstract

We investigate characteristic features of realistic parameter choice for primordial inflation with supersymmetric Higgs inflaton as an example of particle physics inflation model. We discuss constraints from observational results and analyze the degree of fine tuning needed to induce slow-roll inflation for wide range of soft supersymmetry breaking scale. The observed amplitude of density fluctuations implies that the minimal fine tuning for the combined electroweak scale and inflaton flatness predicts the spectral index of 0.950--0.965, which includes the central value from observational data.

Highlights

Recent experimental information such as the Planck satellite results [1] provides cosmological parameters with increasing accuracy, which enables us to perform detailed numerical examination of realistic model parameters in various candidate inflation models [2]
We have investigated inflationary parameter tuning in the supersymmetric Higgs inflation model as an example of particle physics model of primordial inflation
For the electroweak scale and inflaton flatness is given by X = 1.641 × 104 − 2.461 × 104 for e-fold numbers N = 40 − 60, resulting in the spectral index ns = 0.950 − 0.965, which includes the central value of the observed spectral index

Summary

Introduction

Recent experimental information such as the Planck satellite results [1] provides cosmological parameters with increasing accuracy, which enables us to perform detailed numerical examination of realistic model parameters in various candidate inflation models [2]. One of the motivations to investigate numerical aspects of concrete inflation models is to see how the model parameters are chosen or tuned to realize appropriate slow-roll inflation. As for the supersymmetric Higgs degrees of freedom, the quartic contributions to the scalar potential due to gauge interactions are identically zero for specific directions called D-flat directions in the field space of Higgs scalars Along these flat directions, the scalar potential is determined by the soft SUSY breaking terms and higher order non-renormalizable operators appearing in the effective low energy theory.

The inflaton potential

D-flat direction

Inflection point and slow-roll parameters

Inflationary parameter tuning

Conclusion