Local Conformal Symmetry in Physics and Cosmology

TL;DR

This paper develops a locally conformally-invariant formulation of particle physics and gravity, enabling geodesically complete cosmologies and new insights into cosmic evolution driven by the Higgs field within the standard model.

Contribution

It introduces a general form for Weyl-invariant Lagrangians, constructs a conformal standard model coupled to gravity, and demonstrates geodesically complete cosmologies with big crunch-bang transitions.

Findings

Weyl-invariant formulation allows geodesic completeness in cosmology.

Standard model extended with conformal symmetry explains cosmic evolution.

Higgs-driven cosmology without new physics beyond the standard model.

Abstract

We show how to lift a generic non-scale invariant action in Einstein frame into a locally conformally-invariant (or Weyl-invariant) theory and present a new general form for Lagrangians consistent with Weyl symmetry. Advantages of such a conformally invariant formulation of particle physics and gravity include the possibility of constructing geodesically complete cosmologies. We present a conformal-invariant version of the standard model coupled to gravity, and show how Weyl symmetry may be used to obtain unprecedented analytic control over its cosmological solutions. Within this new framework, generic FRW cosmologies are geodesically complete through a series of big crunch - big bang transitions. We discuss a new scenario of cosmic evolution driven by the Higgs field in a \textquotedblleft minimal\textquotedblright% \ conformal standard model, in which there is no new physics beyond the standard model at low energies, and the current Higgs vacuum is metastable as indicated by the latest LHC data.