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We analyze the cosmological implementation of Palatini $f(R)$ theories,constructed with a Nieh-Yan term and solved with respect to the torsion. Weconsider the relevant case of the quadratic correction to the Hilbert-Palatiniaction in the Ricci scalar, mimicking the Starobinsky model of the metricformulation. We point out the emergence of peculiar cosmological scenarios,depending on the sign of such correction, able to reproduce bouncing settingsand to restore the standard Universe dynamics in the late asymptotic limit.Furthermore, we outline the settling of Little-Rip dynamics, which calls for adeeper investigation in order to be regularized via matter creation. Finally,we also show that in our model the Immirzi field is asymptotically frozen intime, resembling the morphology of Loop Quantum Gravity standard formulation.

Big Bounce cosmology for Palatini $R^2$ gravity with a Nieh-Yan term