# Electroweak Vacuum Instability and Renormalized Vacuum Field Fluctuations in Friedmann-Lemaitre-Robertson-Walker Background

## TL;DR

This paper investigates how Higgs vacuum fluctuations in an expanding universe influence electroweak vacuum stability, showing they can both stabilize or destabilize the vacuum depending on the cosmological context and scalar field parameters.

## Contribution

It provides a detailed analysis of Higgs vacuum fluctuations in FLRW backgrounds using adiabatic regularization, revealing their impact on the effective Higgs potential and vacuum stability.

## Key findings

- Higgs fluctuations depend on curvature and scalar masses.
- Vacuum fluctuations can trigger vacuum collapse or stabilize it.
- New cosmological constraints on Higgs-coupled scalar fields.

## Abstract

The cosmological Higgs vacuum stability has been an attractive research subject and it is crucial to accurately follow the development of the Higgs fluctuations. In this work, we thoroughly investigate how the vacuum fluctuations of the Higgs field affect the stability of the electroweak vacuum in Friedmann-Lemaitre-Robertson-Walker (FLRW) background. Adopting adiabatic (WKB) approximation or adiabatic regularization methods, we clearly show that vacuum fluctuations of the Higgs field in the FLRW background depend on the curvature and also masses of the Higgs or other scalar fields. The Higgs fluctuations can generate true vacuum bubbles and trigger off a collapse of the electroweak vacuum. Furthermore we clearly show that the effective Higgs potential in the FLRW background is modified by the Higgs vacuum fluctuations. The vacuum fluctuations of the standard model fields can stabilize or destabilize the effective Higgs potential through backreaction effects. Considering the improved effective Higgs potential with the Higgs vacuum fluctuations $\left< { \delta \phi }^{ 2 } \right>$ in various backgrounds, we provide new cosmological constraints on the mass of the Higgs-coupled scalar fields and a quantitative description of the Higgs stability in the FLRW background.