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Recent results on the non-unitary character of quantum time evolution in the family of Gowdy T3 spacetimes bring the question of whether one should renounce in cosmology to the most sacred principle of unitary evolution. In this work we show that the answer is in the negative. We put forward a full nonperturbative canonical quantization of the polarized Gowdy T3 model that implements the dynamics while preserving unitarity. We discuss possible implications of this result.

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