Thermal Unparticles: A New Form of Energy Density in the Universe

Unparticle $\text{U}$ with scaling dimension $d_{\text{U}}$ has peculiar thermal properties due to its unique phase space structure. We find that the equation of state parameter ${\omega }_{\text{U}}$, the ratio of pressure to energy density, is given by $1\mathrm{/}(2d_{\text{U}}+1)$ providing a new form of energy in our universe. In an expanding universe, the unparticle energy density ${\rho }_{\text{U}}(T)$ evolves dramatically differently from that for photons. For $d_{\text{U}}>1$, even if ${\rho }_{\text{U}}(T_D)$ at a high decoupling temperature $T_D$ is very small, it is possible to have a large relic density ${\rho }_{\text{U}}(T_{\gamma }^0)$ at present photon temperature $T_{\gamma }^0$, large enough to play the role of dark matter. We calculate $T_D$ and ${\rho }_{\text{U}}(T_{\gamma }^0)$ using photon-unparticle interactions for illustration.