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We present a simple generalisation of the $\Lambda$CDM model which on the onehand reaches very good agreement with the present day experimental data andprovides an internal inflationary mechanism on the other hand. It is based onPalatini modified gravity with quadratic Starobinsky term and generalizedChaplygin gas as a matter source providing, besides a current acceleratedexpansion, the epoch of endogenous inflation driven by type III freezesingularity. It follows from our statistical analysis that astronomical datafavors negative value of the parameter coupling quadratic term intoEinstein-Hilbert Lagrangian and as a consequence the bounce instead of initialBig-Bang singularity is preferred.

Inflationary cosmology with Chaplygin gas in Palatini formalism