The QCD nature of Dark Energy

The origin of the observed dark energy could be explained entirely within the standard model, with no new fields required. We show how the low-energy sector of the chiral QCD Lagrangian, once embedded in a non-trivial spacetime, gives rise to a cosmological vacuum energy density which can be can be presented entirely in terms of QCD parameters and the Hubble constant $H$ as $\rho_\Lambda \simeq H \cdot m_q\la\bar{q}q\ra /m_{\eta'} \sim (4.3\cdot 10^{-3} \text{eV})^4$. In this work we focus on the dynamics of the ghost fields that are essential ingredients of the aforementioned Lagrangian. In particular, we argue that the Veneziano ghost, being unphysical in the usual Minkowski QFT, becomes a physical degree of freedom if the universe is expanding. As an immediate consequence, all relevant effects are naturally very small as they are proportional to the rate of expansion $H/ \Lqcd \sim 10^{-41}$. The co-existence of these two drastically different scales ($\Lqcd \sim 100 $ MeV and $H \sim 10^{-33}$ eV) is a direct consequence of the auxiliary conditions on the physical Hilbert space that are necessary to keep the theory unitary. The exact cancellation taking place in Minkowski space due to this auxiliary condition is slightly violated when the system is upgraded to an expanding background. Nevertheless, this "tiny" effect is in fact the driving force accelerating the universe today. We also derive the time dependent equation of state $w(t)$ for the dark energy component which tracks the dynamics of the Veneziano ghost in a FLRW universe. Finally, we comment on how the same physical phenomena can be recovered in Witten's approach to the U(1) problem when the ghost degree of freedom is not even present in the system.