Emergence of the Gambier equation in cosmology

D. Batic, P. Guha, A. Ghose Choudhury

    Research output: Contribution to journalArticlepeer-review


    In this paper, we show how the Gambier equation arises in connection to Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology and a Dark Matter equation of state. Moreover, we provide a correspondence between the Friedmann equations and the Gambier equations that possess the Painlevé property in (2 + 1) dimensions. We also consider special cases of the Gambier G27 equation such as the generalized Pinney equation. For an extended FLRW model with dynamic scalar field as matter model, the Einstein equations correspond to the Milne-Pinney equation which in turn can be mapped to the parametric Gambier equation of second order.

    Original languageBritish English
    Article number2350031
    JournalModern Physics Letters A
    Issue number5
    StatePublished - 20 Feb 2023


    • Ermakov-Painlevé II equation
    • Ermakov-Pinney equation
    • FLRW cosmology
    • Gambier equation
    • generalized Pinney equations


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