  The exact symmetry induced by the global shift of energy scale for the
cosmological constant in the action of matter fields is spontaneously broken by
setting the density of real vacuum energy and explicitly broken by the gravity
that means the existence of Nambu--Goldstone boson, which transforms into the
pseudo-Goldstone boson due to the gravity. We identify this boson with the
inflaton in the Einstein frame of action for the fields, while the breaking is
induced by a non-minimal interaction of boson with the scalar curvature in the
Jordan frame. The role of Galilean symmetry of field equation is emphasized in
the procedure of fixing some terms in the bare action.
