CPT symmetry in the mirror universe

TL;DR

This work develops a CPT-symmetric framework in quantum cosmology for a closed universe by introducing a $3D$-invariant, gauge-invariant time defined from the spectrum of the Hermitian operator $\widehat{W}=\mathcal{D}^2-\Delta$ acting on Dirac bi-spinors, yielding a class of inertial-like reference frames. It formulates CPT for quantum gravity by separately defining $C$, $P$, and $T$ transformations within this framework and constructs a covariant theory of matter gauge fields consistent with charge conjugation. A two-sheeted mirror-universe model with a CPT-symmetric state is developed, employing the no-boundary Hartle–Hawking wave function as a zeroth approximation and an iterative scheme to obtain a CPT-symmetric homogeneous isotropic solution. The approach provides a covariant quantum-gravity formalism with potential implications for baryogenesis near cosmological singularities and explicit gauge-field quantization in quantum cosmology.

Abstract

A model of a two-sheeted universe in the quantum theory of gravity is proposed, based on the definition of 3D invariant and gauge-invariant proper time of the universe. A uniform time in a closed universe is introduced in the class of equivalent reference systems defined by the spectrum of a Hermitian 3D operator on the space of Dirac bi-spinors, the equality to zero of which is equivalent to a system of gravitational constraints. Based on the analogy with the Lorentz-invariant quantum field theory in Minkowski space and the definition of discrete C-, P- and T-transformations separately, the principle of CPT symmetry in a two-sheeted universe is formulated. A covariant quantum theory of matter gauge fields consistent with the charge conjugation operation in a two-sheeted universe is proposed. The CPT symmetric state of a homogeneous isotropic two-sheeted model of the universe is constructed by an iterative method in which the no-boundary Hartle--Hawking wave function is used as a zeroth approximation.