  Considering the conformal scaling gauge symmetry as a fundamental symmetry of
nature in the presence of gravity, a scalar field is required and used to
describe the scale behavior of universe. In order for the scalar field to be a
physical field, a gauge field is necessary to be introduced. A gauge invariant
potential action is constructed by adopting the scalar field and a real
Wilson-like line element of the gauge field. Of particular, the conformal
scaling gauge symmetry can be broken down explicitly via fixing gauge to match
the Einstein-Hilbert action of gravity. As a nontrivial background field
solution of pure gauge has a minimal energy in gauge interactions, the
evolution of universe is then dominated at earlier time by the potential energy
of background field characterized by a scalar field. Since the background field
of pure gauge leads to an exponential potential model of a scalar field, the
universe is driven by a power-law inflation with the scale factor $a(t) \sim
t^p$. The power-law index $p$ is determined by a basic gauge fixing parameter
$g_F$ via $p = 16\pi g_F^2[1 + 3/(4\pi g_F^2) ]$. For the gauge fixing scale
being the Planck mass, we are led to a predictive model with $g_F=1$ and
$p\simeq 62$.

High Energy Physics - Theory