Cosmological evolution in Weyl conformal geometry
  We discuss the cosmological evolution of the Weyl conformal geometry and its
associated Weyl quadratic gravity. The Einstein gravity (with a positive
cosmological constant) is recovered in the spontaneously broken phase of Weyl
gravity; this happens after the Weyl gauge field ($\omega_\mu$) of scale
symmetry, that is part of the Weyl geometry, becomes massive by Stueckelberg
mechanism and decouples. This breaking is a natural result of the cosmological
evolution of Weyl geometry, in the absence of matter. The Weyl quadratic
gravity provides an accelerated expansion of the Universe controlled by the
scalar mode of the $\tilde R^2$ term in the action and by $\omega_0$. The
comparison to the $\Lambda$CDM model shows a very good agreement between these
two models for the (dimensionless) Hubble function $h(z)$ and the deceleration
$q(z)$ for redshifts $z\leq 3$. Therefore, the Weyl conformal geometry and its
associated Weyl quadratic gravity provide an interesting alternative to the
$\Lambda$CDM model and to the Einstein gravity.
