Co-existence of Gravity and Antigravity: The Unification of Dark Matter and Dark Energy

Massive gravity with second and fourth derivatives is shown to give both attractive and repulsive gravities. In contrast to the attractive gravity correlated with the energy-momentum tensor, the repulsive gravity is related to a fixed mass $m_x$, which equals a spin-dependent factor $f_{\sigma }$ times the graviton mass. Therefore, particles with energy below $m_x$ are both dark matter and dark energy: Their overall gravity is attractive with normal matter but repulsive among themselves. Detailed analyses reveal that this unified dark scenario can properly account for the observed dark matter/energy phenomena: galaxy rotation curves, transition from early cosmic deceleration to recent acceleration; and naturally overcome other dark scenarios’ difficulties: the substructure and cuspy core problems, the difference of dark halo distributions in galaxies and clusters, and the cosmic coincidence. Very interestingly, Dirac particles have $f_{\sigma }=1\mathrm{/}\sqrt{2}$, all bosonic matter particles have $f_{\sigma }=0$, and the only exceptional boson is the graviton itself, which may have $f_{\sigma }>1$.