Covariance, relativity, and the proper mass of the universe in the no-boundary wave function

TL;DR

The paper addresses reconciling covariance and relativity in a closed-universe quantum gravity setting by using a Witten-operator formalism to define a discrete family of privileged reference frames. For each frame, the universe's state is formulated as a Euclidean functional integral with no-boundary-like boundary conditions, implemented by an infinite asymptotic Hubble parameter and regularized via a Wick rotation in the cross-section variable $M(x)$. The approach introduces a modified Witten operator and shows that, after Wick rotation, the spectrum becomes discrete and permits a nonzero proper mass for the universe through eigenvalues of a doubled operator $\widehat{\widehat{W}}$. The results hint at a possible link to dark matter phenomenology and outline directions for further exploration.

Abstract

A discrete class of privileged reference frames in a closed universe with identical equations of motion for physical degrees of freedom was found. A representation of the quantum state of the universe in a privileged reference frame was obtained as a Euclidean functional integral with no-boundary conditions. The boundary condition at the Pole, in addition to the smoothness conditions, is the infinite asymptotic behavior of the Hubble parameter. This makes it possible to regularize the functional integral by changing the sign of the expansion energy of the universe. The proposed construction also allows for the addition of a non-zero proper mass of the universe.