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Phase-Space Analysis of an Einstein–Gauss–Bonnet Scalar Field Cosmology

Author

Listed:
  • Alfredo D. Millano

    (Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta 1270709, Chile)

  • Genly Leon

    (Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta 1270709, Chile
    Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa)

  • Andronikos Paliathanasis

    (Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta 1270709, Chile
    Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa)

Abstract

We perform a detailed study of the phase-space of the field equations of an Einstein–Gauss–Bonnet scalar field cosmology for a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime. For the scalar field potential, we consider the exponential function. In contrast, we assume two cases for the coupling function of the scalar field with the Gauss–Bonnet term: the exponential function and the power–law function. We write the field equations in dimensionless variables and study the equilibrium points using normalized and compactified variables. We recover previous results, but also find new asymptotic solutions not previously studied. Finally, these couplings provide a rich cosmological phenomenology.

Suggested Citation

  • Alfredo D. Millano & Genly Leon & Andronikos Paliathanasis, 2023. "Phase-Space Analysis of an Einstein–Gauss–Bonnet Scalar Field Cosmology," Mathematics, MDPI, vol. 11(6), pages 1-52, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1408-:d:1097246
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