  We consider a simple extension of the standard model, which could give a
solution for its $CP$ issues such as the origin of both CKM and PMNS phases and
the strong $CP$ problem. The model is extended with singlet scalars which could
cause spontaneous $CP$ violation to result in these phases at low energy
regions. The singlet scalars could give a good inflaton candidate if they have
a suitable nonminimal coupling with the Ricci scalar. $CP$ issues and inflation
could be closely related through these singlet scalars in a natural way. In a
case where inflaton is a mixture of the singlet scalars, we study reheating and
leptogenesis as notable phenomena affected by the fields introduced in this
extension.
