Quantum flavor vacuum in the expanding universe: A possible candidate for cosmological dark matter?

We analyze fermion mixing in the framework of field quantization in curved spacetime. We compute the expectation value of the energy-momentum tensor of mixed fermions on the flavor vacuum. We consider spatially flat Friedmann-Lemaître-Robertson-Walker metrics, and we show that the energy-momentum tensor of the flavor vacuum is diagonal and conserved. Therefore, it can be interpreted as the effective energy-momentum tensor of a perfect fluid. In particular, assuming a fixed de Sitter background, the equation of state of the fluid is consistent with that of dust and cold dark matter. Our results establish a new link between quantum effects and classical fluids, and indicate that the flavor vacuum of mixed fermions may represent a new component of dark matter.

Figure 1

Squared modulus of the Bogoliubov coefficient $|{\mathrm{\Xi }}_p{|}^2$ as a function of $s$ for sample values of the masses (all in units of $H_0$): (black dotted line) $m_1=0.7$, $m_2=1.4$; (red dashed line) $m_1=1$, $m_2=2$; (blue dot-dashed line) $m_1=10$, $m_2=20$; and (dark orange solid line), $m_1=100$, $m_2=300$. The momentum dependence is implicit in $s=-p\tau$.

Figure 2

Logarithmic scale plot of the energy density ${\rho }_{MIX}={\mathbb{T}}_{\tau }^{\tau (MIX)}$ from Eq. (68) as a function of conformal time $\tau$ for sample values of the parameters. The corresponding coordinate time $t$ is reported above. We have used a cutoff ${\mathcal{K}}_0=246\mathrm{GeV}$ of the order of the electroweak scale, neutrino masses $m_1=15.25H_0,m_2=22.25H_0$, and the expansion rate $H_0={10}^{-3}\mathrm{eV}$.