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Scale Invariance, Mass and Cosmology

E. I. Guendelman
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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 $S = \int L_{1} Φd^4x$ + $\int L_{2}\sqrt{-g}d^4x$ 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 $V(ϕ)$ = $f_{1}e^{αϕ}$ in $L_1$ and $U(ϕ)$ = $f_{2}e^{2αϕ}$ 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.

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E. I. Guendelman. 1999-01-24. Scale Invariance, Mass and Cosmology. https://doi.org/10.1063/1.1301585

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