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 ; depending on the specific form of the self-interaction potential for the field, the constant w can be arbitrary or must be fixed suitably.
Fermi, D., Gengo, M., Pizzocchero, L. (2020). Integrable scalar cosmologies with matter and curvature. NUCLEAR PHYSICS. B, 957, 115095 [10.1016/j.nuclphysb.2020.115095].