Cosmological Landscape and Euclidean Quantum Gravity

TL;DR

This paper explores the quantum creation of the universe via Euclidean path integrals, proposing a cosmological landscape in a mixed state that favors certain universes and constrains the cosmological constant, addressing key issues in quantum gravity.

Contribution

It introduces a new framework for the quantum creation of universes using density matrices and the cosmological bootstrap, showing a bounded landscape of universes and resolving the infrared catastrophe.

Findings

The landscape of universes is limited to a bounded range of the cosmological constant.

Mixed quasi-thermal states are more dynamically favorable than pure Hartle-Hawking states.

Infrared effects eliminate the infrared catastrophe associated with vanishing cosmological constant.

Abstract

Quantum creation of the universe is described by the {\em density matrix} defined by the Euclidean path integral. This yields an ensemble of universes -- a cosmological landscape -- in a mixed quasi-thermal state which is shown to be dynamically more preferable than the pure quantum state of the Hartle-Hawking type. The latter is suppressed by the infinitely large positive action of its instanton, generated by the conformal anomaly of quantum matter. The Hartle-Hawking instantons can be regarded as posing initial conditions for Starobinsky solutions of the anomaly driven deSitter expansion, which are thus dynamically eliminated by infrared effects of quantum gravity. The resulting landscape of hot universes treated within the cosmological bootstrap (the self-consistent back reaction of quantum matter) turns out to be limited to a bounded range of the cosmological constant, which rules out a well-known infrared catastrophe of the vanishing cosmological constant and suggests an ultimate solution to the problem of unboundedness of the cosmological action in Euclidean quantum gravity.