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We discuss the cosmological evolution of the Weyl conformal geometry and itsassociated Weyl quadratic gravity. The Einstein gravity (with a positivecosmological constant) is recovered in the spontaneously broken phase of Weylgravity; this happens after the Weyl gauge field ($\omega_\mu$) of scalesymmetry, that is part of the Weyl geometry, becomes massive by Stueckelbergmechanism and then decouples. This breaking is a natural result of thecosmological evolution of Weyl geometry, in the absence of matter. Ofparticular interest in the analysis is the special limiting case of Weylintegrable geometry. Both this case and the general one provide an acceleratedexpansion 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 $\Lambda$CDMmodel shows a very good agreement to this model for the (dimensionless) Hubblefunction $h(z)$ and the deceleration $q(z)$ for redshift $z\leq 3$. Therefore,the Weyl conformal geometry and its associated Weyl quadratic gravity providean interesting alternative to the $\Lambda$CDM model and to the Einsteingravity.

Cosmological evolution in Weyl conformal geometry