  The non-minimal coupling of a scalar field to the Ricci curvature in a curved
spacetime is unavoidable according to several authors. The coupling constant is
not a free parameter: the prescriptions for the value of the coupling constant
in specific scalar field and gravity theories (in particular in general
relativity) are studied. The results are applied to the most popular
inflationary scenarios of cosmology and their theoretical consistence is
analysed. Certain observational constraints on the coupling constant are also
discussed.
