Unitary evolution in Gowdy cosmology

Abstract

Recent results on the non-unitary character of quantum time evolution in the family of Gowdy T**3 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 T**3 model that implements the dynamics while preserving unitarity. We discuss possible implications of this result.Comment: 5 pages, no figures. V2 discussion expanded, references added. Final version to appear in PR

Quantum Gowdy T 3 model: a uniqueness result

“…In particular, in order to deal with their quantisation, one has to address the question of the unitary equivalence of representations and investigate whether there exist physical criteria that select a preferred one. In the present work, we shall analyse the uniqueness of the Fock quantisation of a particularly interesting midisuperspace model, namely, the model introduced in [11,12] for the description of the linearly polarised Gowdy T 3 cosmologies [13].…”

“…In order to reconcile the quantisation of the linearly polarised Gowdy model with the standard probabilistic interpretation of quantum physics, an alternative nonperturbative canonical quantisation of the model was recently proposed in [11,12]. In this new Fock quantisation, the dynamics is indeed unitary.…”

“…Furthermore, in the present case the translations T α [ † †] are in fact gauge symmetries, because the system is subject to a global constraint which is precisely their generator [11,12]:…”

“…The constraint can then be imposed to obtain the physical Hilbert space. One can show that the dynamics is also unitarily implemented on this space of quantum physical states [11,12].…”

“…In order to arrive at the quantum theory obtained in [11,12] for the Gowdy model, three important choices are made that may affect the final outcome [11,12]. The first one is the choice of deparameterisation, owing to the compact nature of the spatial sections.…”