Scale Invariance, Mass and Cosmology

E. I. Guendelman

doi:10.1063/1.1301585

paper

Scale Invariance, Mass and Cosmology

arXiv:gr-qc/9901067 · doi:10.1063/1.1301585

Abstract

The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. The realizations of scale invariance which are considered, are in the context of a gravitational theory where the action, in the first order formalism, is of the form $S = \int L_{1} Φ d^{4} x$ + $\int L_{2} - g d^{4} x$ where $Φ$ is a density built out of degrees of freedom independent of gravity, which we call the "measure fields". For global scale invariance, a "dilaton" $ϕ$ has to be introduced, with non-trivial potentials $V (ϕ)$ = $f_{1} e^{α ϕ}$ in $L_{1}$ and $U (ϕ)$ = $f_{2} e^{2 α ϕ}$ in $L_{2}$ . This leads to non-trivial mass generation and potential for $ϕ$ . Mass terms for an arbitrary matter field can appear in a scale invariant form both in $L_{1}$ and in $L_{2}$ where they are coupled to different exponentials of the field $ϕ$ . Implications of these results for cosmology having in mind in particular inflationary scenarios, models of the late universe and modified gravitational theories are discussed.

18 pages

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Scale Invariance, Mass and Cosmology

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