Nonminimal Coupling

Abstract

The theory of a scalar field explicitly coupled to the Ricci curvature of spacetime has received so much attention in the literature in different contexts that it deserves special treatment, although it can formally be reduced to a special case of a scalar-tensor theory. The action is

$$ {S^{(NMC)}} = \int {{d^4}x\sqrt { - g} \left[ {\left( {\frac{1}{{2k}} - \frac{\xi }{2}{\phi ^2}} \right)R - \frac{1}{2}{\nabla ^c}\phi {\nabla _c} - V\left( \phi \right)} \right]} + S(m) $$

((7.1))

ξ where is a dimensionless coupling constant. Through most of this chapter, the action S^(m) describing other forms of matter is omitted, since we want to consider regimes in which the nonminimally coupled scalar dominates the cosmic dynamics, for example during inflation.