The cosmological constant from the QCD Veneziano ghost

We suggest that the solution to the cosmological vacuum energy puzzle is linked to the infrared sector of the effective theory of gravity interacting with standard model fields, with QCD fields specifically. We work in the framework of low energy quantum gravity as an effective field theory. In particular, we compute the vacuum energy in terms of QCD parameters and the Hubble constant $H$ such that the vacuum energy is $ε_{vac} \sim H \cdot m_q\la\bar{q}q\ra /m_{η'} \sim (3.6\cdot 10^{-3} \text{eV})^4$, which is amazingly close to the observed value today. The QCD ghost (responsible for the solution of the $U(1)_A$ problem) plays a crucial rôle in the computation of the vacuum energy, because the ghost's properties at very large but finite distances slightly deviate (as $\sim H / \Lqcd $) from their infinite volume Minkowski values. Another important prediction of this framework states that the vacuum energy owes its existence to the asymmetry of the cosmos. Indeed, this effect is a direct consequence of the embedding of our Universe on a non-trivial manifold such as a torus with (slightly) different linear sizes. Such a violation of cosmological isotropy is apparently indeed supported by WMAP, and will be confirmed (or ruled out) by future PLANCK data.

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