On spectrum of vacuum energy

TL;DR

This paper explores the spectral function of vacuum energy, proposing that microscopic degrees of freedom in emergent theories can cancel divergences, with implications for quantum field and gravity models.

Contribution

It introduces the idea that microscopic constituents in emergent theories cancel vacuum energy divergences, contrasting with traditional approaches.

Findings

Spectral functions in condensed matter systems show divergence cancellation.

Emergent gravity models suggest microscopic fields dominate vacuum energy.

Fermionic quasiparticles contribute as in Dirac vacuum.

Abstract

We discuss the problem of the spectral function of vacuum energy. In traditional approach the ultraviolet divergencies of the vacuum energy are cancelled by imposing relations between different quantum fields and their masses. The emergent theories suggest that the microscopic degrees of the underlying quantum vacuum add to the spectral function and their contribution cancels the diverging zero point energy of quantum fields. Examples of the spectral function of the vacuum energy in the condensed-matter systems with relativity emerging at low energy are presented. In the Sakharov induced gravity situation may be even more dramatic: only microscopic (Planck scale) constituent fields contribute to the vacuum energy, while the diverging zero-point energy of emergent quantum field (gravitational field) is missing. On the other hand consideration of the fermionic condensed matter systems suggests that emergent relativistic fermionic quasiparticles contribute in conventional way as Dirac vacuum.