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

TL;DR

The paper tackles the cosmological constant problem arising from quartic UV divergences in vacuum energy within quantum field theory. It introduces a UV-free scheme that uses analytic continuation to produce finite per-field vacuum-energy contributions and defines a scale $\mu_\Lambda$ as a universal reference for vacuum energy. Applying this framework to neutrino fields, it argues that active neutrino vacuum energy can account for the observed dark energy density if neutrino masses fall into a specific normal-ordering window around 10 meV, with detailed mass ranges given. The work emphasizes scale decoupling, showing that heavy fields are exponentially suppressed via a fluctuation factor $f_i = e^{- m_i^2/\mu_\Lambda^2}$, yielding a natural mechanism to avoid large UV contributions. If $\mu_\Lambda$ runs slowly with cosmic evolution, the framework could offer insights into the Hubble tension and provides testable predictions for future neutrino-mass measurements.

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.

Figures (3)

• Figure 1: The vacuum energy in the ripple description.
• Figure 2: The normal ordering neutrinos with the dark energy density $(2.3 ~ \mathrm{meV})^4$. The solid curves are masses of neutrinos with the mass of $\nu_1$ as the input, and the bands with a 5% change in neutrino mass are plotted for a convenient naturalness estimation. The dotted curves are the values of $\mu_\Lambda^{}$ required by the dark energy density with neutrino masses inputted. The region between the two dashed lines is the neutrino mass window.
• Figure 3: The inverted ordering neutrinos with the dark energy density $(2.3 ~ \mathrm{meV})^4$. The solid curves are masses of neutrinos with the mass of $\nu_3$ as the input. The dotted curve is the values of $\mu_\Lambda^{}$ required by the dark energy density.