Scale Invariance, Inflation and the Present Vacuum Energy of the Universe

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 $S=\int L_1\Phi d^{4}x$ + $\int L_2\sqrt{-g}{d}^{4}x$ where $\Phi$ is a density built out of degrees of freedom independent of the metric. For global scale invariance, a "dilaton" $\varphi$ has to be introduced, with non-trivial potentials $V(\varphi )$ = $f_1{e}^{\alpha \varphi }$ in $L_1$ and $U(\varphi )$ = $f_2{e}^{2\alpha \varphi }$ in $L_2$. This leads to non-trivial mass generation and a potential for $\varphi$ which is interesting for inflation. The model after ssb can be connected to the induced gravity model of Zee, which is a successful model of inflation. Models of the present universe and a natural transition from inflation to a slowly accelerated universe at late times are discussed.

Contribution to the conference "Energy Densities in the Universe", Les Arcs, France, January 2000