Causality and the Arrow of Time in the Branch-Cut Cosmology

TL;DR

This paper explores the connection between quantum time evolution, the cosmic arrow of time, and causality in a branch-cut universe, proposing a novel calculation of universe branches to address causality issues.

Contribution

It introduces a new approach to calculating the number of universe branches in branch-cut cosmology to reconcile causality with global and local cosmic time.

Findings

Number of branches comparable to 60 e-folds of contraction

Causality achieved in bouncing cosmological models

Identification of imaginary temporal component with the arrow of time

Abstract

We basis our initial analysis of the arrow of time on a relationship between the time evolution operator of quantum system and the time-independent density operator which describes the equilibrium state of a many-particle system at temperature $T$. We highlight through this analysis the identification of the imaginary temporal component of the branch-cut complex cosmic form factor with the direction in which the time-parameter flows globally, or the arrow of time. As a novelty, in this work we calculate the number of branches in the branch-cut universe to achieve causality involving the global time of evolution of the universe and the local time of travel of the light around each Hubble horizon. The preliminary result obtained is comparable to 60 e-folds of contraction in the FLRW cosmic scale factor $a(t) $ to overcome causality achieved in the bouncing model.