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Some Cosmological Applications of Two Measures Theory

E. I. Guendelman·A. B. Kaganovich
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Abstract

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} Φd^4x + \int L_{2}\sqrt{-g}d^4x where Φis a density built out of degrees of freedom independent of the metric. For global scale invariance, a "dilaton" ϕhas 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. In the effective Einstein frame, this leads to a non-trivial ϕpotential (of the Morse type) which has a flat region with energy density f_{1}^{2}/4f_{2} as ϕ\to\infty. The addition of an R^{2} term produces an effective potential with two connected flat regions: one of the Planck scale, that can be responsible for early inflation, and another for the description of the present universe.

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E. I. Guendelman, A. B. Kaganovich. 2004-03-03. Some Cosmological Applications of Two Measures Theory. https://arxiv.org/abs/gr-qc/0403017

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