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- W2510247536 abstract "The problem of classification of the Einstein--Friedman cosmological Hamiltonians $H$ with a single scalar inflaton field $varphi$ that possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $H=0$ is considered. Necessary and sufficient conditions for the existence of first, second, and third degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $V(varphi)$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in a parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described and sporadic superintegrable cases are discussed." @default.
- W2510247536 created "2016-09-16" @default.
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- W2510247536 date "2017-05-08" @default.
- W2510247536 modified "2023-10-18" @default.
- W2510247536 title "Integrable cosmological potentials" @default.
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- W2510247536 doi "https://doi.org/10.1007/s11005-017-0962-y" @default.
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