Elsevier, Physics Letters A, 20-21(379), p. 1304-1308, 2015
DOI: 10.1016/j.physleta.2015.02.044
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Scalar-tensor Cosmologies can be dealt under the standard of the Hojman conservation theorem that allows to fix the form of the coupling $F(ϕ)$, of the potential $V(ϕ)$ and to find out exact solutions for related cosmological models. Specifically, the existence of a symmetry transformation vector for the equations of motion gives rise to a Hojman conserved quantity on the corresponding minisuperpace and exact solutions for the cosmic scale factor $a$ and the scalar field $ϕ$ can be achieved. In particular, we take advantage of the fact that minimally coupled solutions, previously obtained in the Einstein frame, can be conformally transformed in non-minimally coupled solutions in the Jordan frame. Some physically relevant examples are worked out. ; Comment: 6 pages, 4 figures, to appear in Phys. Lett. A