Gravitational corrections to electroweak vacuum decay: metric vs. Palatini

Abstract

We consider the standard Einstein-Hilbert-Higgs action where the Higgs field couples nonminimally with gravity via the term $\xi h^2\mathcal{R}$, and investigate the stability of the electroweak vacuum in the presence of gravitational corrections in both the metric and Palatini formulations of gravity. In order to identify the differences between the two formalisms analytically, we follow a perturbative approach in which the gravitational corrections are taken into consideration via a leading order expansion in the gravitational coupling constant. Our analysis shows that in the Palatini formalism, the well-known effect of gravity suppressing the vacuum decay probability, becomes milder in comparison with the metric case for any value of the nonminimal coupling $\xi$. Furthermore, we have found that in the Palatini formalism, the positivity of the gravitational corrections, which is a necessary requirement for the unitarity of the theory, entails the lower bound $\xi >-1/12$.

typos corrected

References in corpus (9)

• The Standard Model Higgs boson as the inflaton
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Spacetime curvature and the Higgs stability during inflation
• Gravitational corrections to Standard Model vacuum decay
• Electroweak Vacuum Stability in light of BICEP2
• Inflationary cosmology and the standard model Higgs with a small Hubble induced mass
• False Vacuum Decay Catalyzed by Black Holes
• Spacetime Dynamics of a Higgs Vacuum Instability During Inflation
• Standard Model vacuum decay in a de Sitter Background

Cited by in corpus (10)

• Cosmological phase transitions: from perturbative particle physics to gravitational waves
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Electroweak vacuum decay in metric-affine gravity
• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
• Gravity-improved metastability bounds for the Type-I Seesaw Mechanism
• Beyond (and back to) Palatini quadratic gravity and inflation
• General Einstein-Cartan quadratic gravity with derivative couplings
• Natural inflation in Palatini $F(R,X)$
• Cosmic inflation in metric-affine gravity
• Inflationary assessment of $F(\mathcal{R},\tilde{\mathcal{R}})$ Einstein-Cartan models