Dynamics of three-form dark energy with dark matter couplings

Three-form field can give rise to viable cosmological scenarios of dark energy with potentially observable signatures distinct from standard single scalar field models. In this study, the background dynamics of three-form cosmology are investigated. Our analysis suggests that the potential of three-form field should be runaway. We also investigate the possibility to solve the coincidence problem by using the coupling of three-form field to dark matter. Four types of coupling form are examined and we find that the coupling of the form $Q = \sqrt{6}\Gamma (\dot{X} + 3HX)/\kappa$ provides the possibility to solve the coincidence problem.