Complex Loop Quantum Cosmology

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We study in the context of loop quantum cosmology the effect of the analytic continuation that sends the Barbero-Immirzi parameter to a purely imaginary value. We show that this construction leads once again to a bouncing scenario, in which however the contracting and expanding phases on each side of the bounce are not symmetrical. Moreover, the minimal volume reached by the universe and the critical matter density become naturally independent of the Barbero-Immirzi parameter. This analytic continuation was first proposed in the context of black hole entropy calculation, and constitutes a proposal for defining a theory of self-dual quantum gravity in terms of the complex Ashtekar connection and for solving the so-called reality conditions. We expect that the systematic investigation of this analytic continuation in various setups will eventually lead to new insights on the status of the quantum states of complex Ashtekar gravity.