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A new force is proposed in order to explain galactic rotation curves. CPT ischosen as the underlying symmetry of the new force because it is a universalspacetime symmetry. Local CPT transformations are presented for the Dirac field(matter) and the vierbein describing curved spacetime. A nonvanishing variationof the Dirac action in curved spacetime is thus derived. Because the metricspin connection of general relativity cannot accommodate the variation inducedby the local CPT symmetry, a new gauge field is introduced. The transformationof the new field is derived which implies the new field is massless.Experimental speculations based on the zero mass of the new gauge field arepresented. It is shown that one type of Yang-Mills Lagrangian density is notinvariant under local CPT transformations.

Gauge CPT as a Possible Alternative to the Dark Matter Hypothesis