Scale Invariance and Vacuum Energy

TL;DR

This paper explores scale-invariant gravitational theories with a dilaton field, proposing mechanisms for mass generation and potential explanations for cosmic acceleration and coincidences.

Contribution

It introduces a scale-invariant gravitational framework with a dilaton, leading to novel mass generation mechanisms and implications for cosmology.

Findings

Mass generation through scale invariance mechanisms

Potential for explaining cosmic acceleration

Dilaton field dynamics relevant for inflation

Abstract

The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. Scale invariance is considered in the context of a gravitational theory where the action, in the first order formalism, is of the form $S = \int L_{1} \Phi d^4x$ + $\int L_{2}\sqrt{-g}d^4x$ where $\Phi$ is a density built out of degrees of freedom independent of the metric. For global scale invariance, a "dilaton" $\phi$ has to be introduced, with non-trivial potentials $V(\phi)$ = $f_{1}e^{\alpha\phi}$ in $L_1$ and $U(\phi)$ = $f_{2}e^{2\alpha\phi}$ in $L_2$. This leads to non-trivial mass generation and a potential for $\phi$ which is interesting for new inflation. Scale invariant mass terms for fermions lead to a possible explanation of the present day accelerated universe and of cosmic coincidences.