2, derivative coupling M Ougocy, Fpo, Gpa s-) 1, obeys the shift symmetry 9>0+const which guarantees the flatness of the potential 2, propagates spin-dependent force, short range much weaker constraint from astrophysics M≥10 GeV PDG(2002) Violates Lorentz and cPt symmetry because <O0>=≠0 (CPT) oo (cPt)=(CPt)O(CPt)=-oo cosmological CPT violation2, derivative coupling: cosmological CPT violation! 1, obeys the shift symmetry which guarantees the flatness of the potential. 2, propagates spin-dependent force, short range, much weaker constraint from astrophysics PDG(2002) Violates Lorentz and CPT symmetry because  → + const.  0  =  0  ( , , ,...)     O  F G M c  1 0 1 0 0 (CPT)   O (CPT) =  (CPT) O (CPT) = −  O − − M GeV 10 10