  We study the effect of finite chemical potential on the d-density wave state
that has been proposed to explain the pseudogap phenomena in underdoped
cuprates. We find that the specific heat anomaly at the transition temperature,
below which the d-density wave state forms, gets weaker when finite chemical
potential is introduced. This provides a useful ground for the proper
interpretation of the specific heat measurement in regard to the existence of
the d-density wave state below the pseudogap temperature. Further increase of
the chemical potential leads to an incommensurate orbital antiferromagnetic
state before the system eventually turns into the normal state. This is an
inhomogeneous state characterized by novel charge ordering and an analog of the
Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state in superconductivity.
