Dark Energy Is the Cosmological Quantum Vacuum Energy of Light Particles—The Axion and the Lightest Neutrino

We uncover the general mechanism and the nature of today’s dark energy (DE). This is only based on well-known quantum physics and cosmology. We show that the observed DE today originates from the cosmological quantum vacuum of light particles, which provides a continuous energy distribution able to reproduce the data. Bosons give positive contributions to the DE, while fermions yield negative contributions. As usual in field theory, ultraviolet divergences are subtracted from the physical quantities. The subtractions respect the symmetries of the theory, and we normalize the physical quantities to be zero for the Minkowski vacuum. The resulting finite contributions to the energy density and the pressure from the quantum vacuum grow as $loga\left(t\right)$, where $a\left(t\right)$ is the scale factor, while the particle contributions dilute as $1/a^3\left(t\right)$, as it must be for massive particles. We find the explicit dark energy equation of state of today to be $P=w\left(z\right)\mathcal{H}$: it turns to be slightly $w\left(z\right)<-1$ with $w\left(z\right)$ asymptotically reaching the value $-1$ from below. A scalar particle can produce the observed dark energy through its quantum cosmological vacuum provided that (i) its mass is of the order of ${10}^{-3}$ eV = 1 meV, (ii) it is very weakly coupled, and (iii) it is stable on the time scale of the age of the universe. The axion vacuum thus appears as a natural candidate. The neutrino vacuum (especially the lightest mass eigenstate) can give negative contributions to the dark energy. We find that $w(z=0)$ is slightly below $-1$ by an amount ranging from $(-1.5\times {10}^{-3})$ to $(-8\times {10}^{-3})$ and we predict the axion mass to be in the range between 4 and 5 $\mathrm{meV}$. We find that the universe will expand in the future faster than the de Sitter universe as an exponential in the square of the cosmic time. Dark energy today arises from the quantum vacuum of light particles in FRW cosmological space-time in an analogous way to the Casimir vacuum effect of quantum fields in Minkowski space-time with non-trivial boundary conditions.