The Dirac Field at the Future Conformal Singularity

TL;DR

This paper investigates how the Dirac wavefunction behaves near the future conformal singularity in cosmological spacetimes, revealing boundary conditions that could have observable consequences today.

Contribution

It introduces a boundary condition for the Dirac wavefunction at the future conformal singularity, impacting its spectral properties and potential observability.

Findings

Only two of four bi-spinor components survive at the boundary

Geodesics experience a drag towards the Hubble frame near the singularity

A genuine boundary condition at the singularity influences the wavefunction's spectral decomposition

Abstract

We examine in detail the effect of the conformal factor associated with the Friedmann-Robertson-Walker spacetimes on the discrete symmetries usually present in the Dirac theory and analyze the behavior of the Dirac wavefunction near the future conformal singularity. We find that only two of the 4 bi-spinor components survive to the boundary, one effect of which is to cause the geodesics to experience a drag towards the Hubble frame. We then present arguments for the existence of a genuine boundary condition on the wavefunction at the future conformal singularity based upon the assumption there is no redundant copy of the universe in the post-conformal singularity era. This future boundary condition affects the spectral decomposition of the wavefunction, and this maybe locally testable at the present time.