Emergence of the Gambier equation in cosmology

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

doi:10.1142/S0217732323500311

Emergence of the Gambier equation in cosmology

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

Mathematics

Diamond Harbour Women’s University

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	British English
Article number	2350031
Journal	Modern Physics Letters A
Volume	38
Issue number	5
DOIs	https://doi.org/10.1142/S0217732323500311
State	Published - 20 Feb 2023

Keywords

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

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10.1142/S0217732323500311

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title = "Emergence of the Gambier equation in cosmology",

abstract = "In this paper, we show how the Gambier equation arises in connection to Friedmann-Lema{\^i}tre-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 Painlev{\'e} 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.",

keywords = "Ermakov-Painlev{\'e} II equation, Ermakov-Pinney equation, FLRW cosmology, Gambier equation, generalized Pinney equations",

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AU - Choudhury, A. Ghose

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N2 - 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.

AB - 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.

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KW - FLRW cosmology

KW - Gambier equation

KW - generalized Pinney equations

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VL - 38

JO - Modern Physics Letters A

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Emergence of the Gambier equation in cosmology

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