A try for dark energy in quantum field theory: The vacuum energy of neutrino field

TL;DR

This paper proposes a UV-free scheme to evaluate neutrino vacuum energy contributions to dark energy, suggesting neutrino masses around 10 meV can naturally explain observed dark energy density, favoring normal ordering.

Contribution

It introduces a UV-free evaluation method for vacuum energy and links neutrino mass scales to dark energy, addressing the cosmological constant problem.

Findings

Neutrino vacuum energy can account for dark energy density.

Active neutrino masses around 10 meV fit observational data.

Normal neutrino mass ordering is favored by naturalness.

Abstract

The quartic-divergent vacuum energy poses an ultraviolet (UV) challenge (the cosmological constant problem) in probing the nature of dark energy. Here we try to evaluate the contribution of the vacuum energy to dark energy with a method of the UV-free scheme. The result indicates that it is not a problem in the UV region but a question of the contributions of heavy fields being suppressed. Then, we explore an effective description via scale decoupling. The parameter spaces suggest that the vacuum energy of active neutrino fields can naturally meet the observation of dark energy density, and a neutrino with a typical mass $\sim$ 10 meV $(10^{-3}$ eV) is expected. The normal ordering neutrinos are preferred by naturalness, and the neutrino mass window set by dark energy is 6.3 meV $\lesssim m_1 \lesssim$ 16.3 meV, 10.7 meV $\lesssim m_2 \lesssim$ 18.4 meV, 50.5 meV $\lesssim m_3 \lesssim$ 52.7 meV.