Gauge theory in de Sitter space-time from a holographic model

Yang-Mills theory with flavor quarks in the dS${}_4$ is studied through the dual supergravity in the AdS${}_5\times S^5$ background with non-trivial dilaton and axion. The flavor quarks are introduced by embedding a probe D7 brane. We find that the dynamical properties of YM theory in the dS${}_4$ are similar to the case of the finite temperature theory given by the 5d AdS-Schwarzschild background. In the case of dS${}_4$, however, contrary to the finite temperature case, the gauge field condensate plays an important role on the dynamical properties of quarks. We also give the quark-antiquark potential and meson spectra to find possible quark-bound states. And we arrive at the conclusion that, while the quarks are not confined in the dS${}_4$, we could find stable meson states at very small cosmological constant as expected in the present universe. But there would be no hadrons at early universe as in the inflation era.