Differences between scalar field and scalar density field solutions

Differences between scalar field and scalar density solutions are explored using a Robertson-Walker (RW) metric, and a nonrelativistic Hamiltonian is derived for a scalar density field in the post-newtonian approximation. The results are compared with those of a scalar field. The expanding universe in a RW metric and a post-newtonian solution of the Klein-Gordon equation are discussed separately. © 2012 Published by NRC Research Press.