A programme for a problem-free cosmology within the framework of a rich class of scalar-tensor theories

A search for a problem-free cosmology within the framework of an effective nonminimally coupled scalar-tensor theory is suggested. With an appropriate choice of couplings in variants of a Lee-Wick model (as also in a model su pporting Q-ball solutions), non-topological solutions (NTSs), varying in si ze up to 10 kpc to 1 Mpc can exist. We explore the properties of a 'toy' Mi lne model containing a distribution of NTS domains. The interior of these d omains would be regions where effective gravitational effects would be indi stinguishable from those expected in standard Einstein theory. For a large class of non-minimal coupling terms and the scalar effective potential, the effective cosmological constant vanishes identically. The model passes cla ssical cosmological tests and we describe reasons to expect it to fare well as regards nucleosynthesis and structure formation.