Scalar fields in curved spacetimes

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Abstract
The author examines the most general theory describing a real scalar field coupled to Einstein gravity in four dimensions. The author shows that the stress tensor of the scalar field always has the structure of a fluid stress tensor. In the case that the scalar field is minimally coupled to gravity, this reduces to a perfect-fluid structure. In addition, the author obtains a generally non-trivial form of the Bianchi identities for this theory, investigates the kinematics of the scalar field and shows how to extend the analysis to include complex scalars and scalar multiplets. Finally, the author discusses the ground-state solutions of the theory, with special attention given to the case when the scalar field potential is polynomial in the fields. The author shows that the gravity-scalar coupling has interesting consequences for the spontaneous breakdown of gauge symmetries and for the observable value of the cosmological constant.

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