Cosmological spacetimes balanced by a scale covariant scalar field

TL;DR

This paper explores a scale-invariant cosmological model using Weyl geometry and a scalar field, showing how it can produce stable universe solutions and align with some observational data like supernovae.

Contribution

It introduces a Weyl geometric, scale-invariant cosmological model with a solvable scalar field equation and demonstrates its potential to explain universe stability and match observational data.

Findings

Scalar field energy-momentum tensor includes vacuum-like and dark matter terms.

Models can maintain stable equilibrium under certain parameters.

Preliminary observational data comparison shows promising empirical properties.

Abstract

A scale invariant, Weyl geometric, Lagrangian approach to cosmology is explored, with a a scalar field phi of (scale) weight -1 as a crucial ingredient besides classical matter \cite{Tann:Diss,Drechsler:Higgs}. For a particularly simple class of Weyl geometric models (called {\em Einstein-Weyl universes}) the Klein-Gordon equation for phi is explicitly solvable. In this case the energy-stress tensor of the scalar field consists of a vacuum-like term Lambda g_{mu nu} with variable coefficient Lambda, depending on matter density and spacetime geometry, and of a dark matter like term. Under certain assumptions on parameter constellations, the energy-stress tensor of the phi-field keeps Einstein-Weyl universes in locally stable equilibrium. A short glance at observational data, in particular supernovae Ia (Riess ea 2007), shows interesting empirical properties of these models.