Integrable scalar cosmologies with matter and curvature

We show that several integrable (i.e., exactly solvable) scalar cosmologies considered by Fré, Sagnotti and Sorin (Nuclear Physics B 877(3) (2013), 1028–1106) can be generalized to include cases where the spatial curvature is not zero and, besides a scalar field, matter or radiation are present with an equation of state p(m)=wρ(m); depending on the specific form of the self-interaction potential for the field, the constant w can be arbitrary or must be fixed suitably.