Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-11-08
Found.Phys. 31 (2001) 1019-1037
Physics
High Energy Physics
High Energy Physics - Theory
contribution to the IARD2000 conference, Bar Ilan University, Ramat Gan, Israel, 26-28 June 2000
Scientific paper
Scale invariance is considered in the context of gravitational theories 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 the volume element $\Phi d^4x$ is 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 inflation. Interpolating models for natural transition from inflation to a slowly accelerated universe at late times appear naturally. This is also achieved for "Quintessential models", which are scale invariant but formulated with the use of volume element $\Phi d^4x$ alone. For closed strings and branes (including the supersymmetric cases), the modified measure formulation is possible and does not require the introduction of a particular scale (the string or brane tension) from the begining but rather these appear as integration constants.
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