From DeWitt initial condition to Cosmological Quantum Entanglement

TL;DR

This paper explores a gravity-anti-gravity linear dilaton model that describes eternal inflation and quantum cosmology, revealing how boundary conditions influence the universe's initial state and the role of entanglement.

Contribution

It introduces a novel GaG-odd linear dilaton action and analyzes its implications for boundary conditions and wave functions in quantum cosmology.

Findings

Weak Big Bang boundary condition with GaG-odd wave function

Strong boundary condition favors GaG-even entangled wave function

Most probable scale factor and dilaton values form a specific grid pattern

Abstract

A gravity-anti-gravity (GaG) odd linear dilaton action offers an eternal inflation evolution governed by the unified (cosmological constant plus radiation) equation of state $\rho-3P=4\Lambda$. At the mini superspace level, a 'two-particle' variant of the no-boundary proposal, notably 'one-particle' energy dependent, is encountered. While a GaG-odd wave function can only host a weak Big Bang boundary condition, albeit for any $k$, a strong Big Bang boundary condition requires a GaG-even entangled wave function, and singles out $k=0$ flat space. The locally most probable values for the cosmological scale factor and the dilaton field form a grid $\{a^2,a\phi\}\sim\sqrt{4n_1+1}\pm\sqrt{4n_2+1}$.