Quantum String Cosmology

Maurizio Gasperini

doi:10.3390/universe7010014

Abstract

We present a short review of possible applications of the Wheeler-De Witt equation to cosmological models based on the low-energy string effective action, and characterised by an initial regime of asymptotically flat, low energy, weak coupling evolution. Considering in particular a class of duality-related (but classically disconnected) background solutions, we shall discuss the possibility of quantum transitions between the phases of pre-big bang and post-big bang evolution. We will show that it is possible, in such a context, to represent the birth of our Universe as a quantum process of tunneling or “anti-tunneling” from an initial state asymptotically approaching the string perturbative vacuum.

Highlights

In the standard cosmological context the Universe is expected to emerge from the big bang singularity and to evolve initially through a phase of very high curvature and density, well inside the quantum gravity regime
In the class of string cosmology models considered in this paper, in contrast, the initial state is uniquely determined by a fixed choice of pre-big bang evolution, which starts asymptotically from the string perturbative vacuum and which, in this way, unambiguously determines the initial “wave function” of the Universe and the subsequent transition probabilities
In this paper we report the results of previous works, based on the study of the Wheeler–De Witt (WDW) equation [18,19] in the “minisuperspace” associated with a class of cosmological backgrounds compatible with the dynamics the low-energy string effective action [20,21,22,23,24,25,26]

Summary

Introduction

In the standard cosmological context the Universe is expected to emerge from the big bang singularity and to evolve initially through a phase of very high curvature and density, well inside the quantum gravity regime. In this paper we report the results of previous works, based on the study of the Wheeler–De Witt (WDW) equation [18,19] in the “minisuperspace” associated with a class of cosmological backgrounds compatible with the dynamics the low-energy string effective action [20,21,22,23,24,25,26] It is possible, in such a context, to obtain a non-vanishing transition probability between two different geometrical configurations—in particular, from a prebig bang to a post-big bang state—even if they are classically disconnected by a spacetime singularity.

The Wheeler-De Witt Equation for the Low-Energy String Effective Action

Quantum Scattering of the Wheeler-De Witt Wave Function in Minisuperspace

Birth of the Universe as a Tunnelling from the String Perturbative Vacuum

Birth of the Universe as Anti-Tunnelling from the String Perturbative Vacuum

Conclusions