Running non-minimal inflation with stabilized inflaton potential

Nobuchika Okada,Digesh Raut

doi:10.1140/epjc/s10052-017-4799-4

Nobuchika Okada, Digesh Raut

Open Access

https://doi.org/10.1140/epjc/s10052-017-4799-4

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Abstract

In the context of the Higgs model involving gauge and Yukawa interactions with the spontaneous gauge symmetry breaking, we consider lambda phi ^4 inflation with non-minimal gravitational coupling, where the Higgs field is identified as the inflaton. Since the inflaton quartic coupling is very small, once quantum corrections through the gauge and Yukawa interactions are taken into account, the inflaton effective potential most likely becomes unstable. In order to avoid this problem, we need to impose stability conditions on the effective inflaton potential, which lead to not only non-trivial relations amongst the particle mass spectrum of the model, but also correlations between the inflationary predictions and the mass spectrum. For concrete discussion, we investigate the minimal B-L extension of the standard model with identification of the B-L Higgs field as the inflaton. The stability conditions for the inflaton effective potential fix the mass ratio amongst the B-L gauge boson, the right-handed neutrinos and the inflaton. This mass ratio also correlates with the inflationary predictions. In other words, if the B-L gauge boson and the right-handed neutrinos are discovered in the future, their observed mass ratio provides constraints on the inflationary predictions.

Highlights

The Planck 2015 results [5] have set an upper bound on the tensor-to-scalar ratio as r 0.11 while the best fit value for the spectral index is 0.9655 ± 0.0062 at 68% CL
We have considered the general Higgs model with the gauge and Yukawa interactions with the spontaneous gauge symmetry breaking
Once we take quantum corrections, the effective inflaton potential most likely becomes unstable. This is because the inflaton quartic coupling is extremely small in a large portion of the parameters space and the effective potential is controlled by the gauge and Yukawa couplings independently of the quartic coupling

Summary

Introduction

The Planck 2015 results [5] have set an upper bound on the tensor-to-scalar ratio as r 0.11 while the best fit value for the spectral index (ns) is 0.9655 ± 0.0062 at 68% CL. The SM Higgs inflation [9,10,11,12,13,14,15,16,17,18] is nothing but this scenario, where the SM Higgs boson plays the role of inflaton with non-minimal gravitational coupling. In order to explicitly show the mass relation and the correlation between the particle mass spectrum and inflationary predictions, we take the minimal B − L model as an example This model is a very simple, well-motivated extension of the SM, where the global B − L (baryon number minus lepton number) in the SM is gauged. We briefly review the λφ inflation with non-minimal gravitational coupling at the tree level, and discuss the inflationary predictions in the light of the Planck 2015 results.

Non-minimal λφ4 inflation at tree level

Inflationary predictions and low energy observables

Reheating after inflation

Conclusions