Scale Invariance, Inflation and the Present Vacuum Energy of
the Universe
E.I.Guendelman
Department of Physics, Ben Gurion University,
Beer Sheva 84105, Israel
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 $S =
\int L_{1} \Phi d^4x$ + $\int L_{2}\sqrt{-g}d^4x$ where $\Phi$ is a
density built out of degrees of freedom 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. 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.