Indifference boundary condition for the universe

Description

Title: Indifference boundary condition for the universe

Author: Ding Jia

Abstract: Path integral models for quantum cosmology need boundary condition. Since the no-boundary and tunneling proposals face stubborn difficulties, it is worth exploring alternatives. An old proposal due to Suen and Young posits that all possible initial boundary configurations should be summed over indifferently. The proposal has the merit of being applicable to and beyond symmetry-reduced models, and is suitable for theories based on non-singular Lorentzian path integrals. However, it also upholds a past-future asymmetry, requires a preferred basis, and lacks a clear prescription for empirical predictions. Here we extend the indifference proposal in three ways to develop the idea. Firstly, future boundary conditions are incorporated alongside past conditions. This eliminates the inherent past-future asymmetry, even though the original proposal can be recovered as a special case. Secondly, a mixed sum is proposed to realize the idea for an indifferent sum. This avoids the need to specify a preferred basis for Suen and Young’s original proposal based on a pure sum. Lastly, a minimal prescription is employed to derive empirical predictions. In an application to the de Sitter minisuperspace model, it is shown how the most probable outcome for an observation of the squared scale factor aligns with the saddle points that solve the classical equation of motion. In the picture emerging from the indifference boundary conditions, Big Bang and Big Bounce are not exclusive alternatives. Instead, the path integral includes geometries realizing both possibilities.

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Version history

• Original versions: Article v1.0; Notebook v1.0