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 \textbf{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 $p^{(m)} = w\, ρ^{(m)}$; depending on the specific form of the self-interaction potential for the field, the constant $w$ can be arbitrary or must be fixed suitably.

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