A stochastic quasi-classical wavefunction of the Universe from the third quantization procedure

Abstract

(abbreviated) We study quantized solutions of WdW equation describing a closed FRW universe with a $\Lambda$ term and a set of massless scalar fields. We show that when $\Lambda \ll 1$ in the natural units and the standard $in$-vacuum state is considered, either wavefunction of the universe, $\Psi$, or its derivative with respect to the scale factor, $a$, behave as random quasi-classical fields at sufficiently large values of $a$, when $1\ll a\ll e^{\frac{2}{3\Lambda }}$ or $a\gg e^{\frac{2}{3\Lambda }}$, respectively. Statistical r.m.s value of the wavefunction is proportional to the Hartle-Hawking wavefunction for a closed universe with a $\Lambda$ term. Alternatively, the behaviour of our system at large values of $a$ can be described in terms of a density matrix corresponding to a mixed state, which is directly determined by statistical properties of $\Psi$. It gives a non-trivial probability distribution over field velocities. We suppose that a similar behaviour of $\Psi$ can be found in all models exhibiting copious production of excitations with respect to $out$-vacuum state associated with classical trajectories at large values of $a$. Thus, the third quantization procedure may provide a 'boundary condition' for classical solutions of WdW equation.

To be published in PRD, several misprints have been corrected and a reference has been added

References in corpus (2)

• Group field cosmology: a cosmological field theory of quantum geometry
• Non-linear (loop) quantum cosmology

Cited by in corpus (1)

• Super-group field cosmology in Batalin-Vilkovisky formulation