Constraints on the Cosmological Constant due to Scale Invariance

TL;DR

This paper explores how local scale invariance in the standard model leads to vanishing contributions from massless gauge and fermion fields to the cosmological constant, with the non-zero value arising from symmetry breaking.

Contribution

It demonstrates that massless gauge and fermion fields do not contribute to the cosmological constant in a scale-invariant standard model, highlighting the role of symmetry breaking.

Findings

Massless gauge fields contribute zero to the cosmological constant.

Massless fermion fields also yield null contribution.

The effective cosmological constant arises from cosmological symmetry breaking.

Abstract

We consider the standard model with local scale invariance. The theory shows exact scale invariance of dimensionally regulated action. We show that massless gauge fields, which may be abelian or non-abelian, lead to vanishing contribution to the cosmological constant in this theory. This result follows in the quantum theory, to all orders in the gauge couplings. However we have not considered contributions higher orders in the gravitational coupling. Similarly we also find that massless fermion fields yield null contribution to the cosmological constant. The effective cosmological constant in this theory is non-zero due to the phenomenon of cosmological symmetry breaking, which also gives masses to all the massive fields, besides generating the Planck mass. We find a simple relationship between the curvature scalar and the vacuum value of the Higgs field in the limit when we ignore all other contributions to the energy density besides the vacuum energy.