  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 then decouples. This breaking is a natural result of the
cosmological evolution of Weyl geometry, in the absence of matter. Of
particular interest in the analysis is the special limiting case of Weyl
integrable geometry. Both this case and the general one provide an accelerated
expansion of the Universe, controlled by the scalar mode of the $\tilde R^2$
term in the action and by $\omega_0$. Their comparison to the $\Lambda$CDM
model shows a very good agreement to this model for the (dimensionless) Hubble
function $h(z)$ and the deceleration $q(z)$ for redshift $z\leq 3$. 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.
