Cosmological phase-space analysis of f(G)-theories of gravity
Papagiannopoulos G. Luongo O. Leon G. Paliathanasis A.
July 2025Elsevier B.V.
Journal of High Energy Astrophysics
2025#47
The impact of topological terms that modify the Hilbert-Einstein action is here explored by virtue of a further f(G) contribution. In particular, we investigate the phase-space stability and critical points of an equivalent scalar field representation that makes use of a massive field, whose potential is function of the topological correction. To do so, we introduce to the gravitational Action Integral a Lagrange multiplier and model the modified Friedmann equations by virtue of new non-dimensional variables. We single out dimensionless variables that permit a priori the Hubble rate change of sign, enabling regions in which the Hubble parameter either vanishes or becomes negative. In this respect, we thus analyze the various possibilities associated with a universe characterized by such topological contributions and find the attractors, saddle points and regions of stability, in general. The overall analysis is carried out considering the exponential potential first and then shifting to more complicated cases, where the underlying variables do not simplify. We compute the eigenvalues of our coupled differential equations and, accordingly, the stability of the system, in both a spatially-flat and non-flat universe. Quite remarkably, regardless of the spatial curvature, we show that a stable de Sitter-like phase that can model current time appears only a small fraction of the entire phase-space, suggesting that the model under exam is unlikely in describing the whole universe dynamics, i.e., the topological terms appear disfavored in framing the entire evolution of the universe.
Equilibrium points , f(G)-gravity , Gauss-Bonnet
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Department of Physics, National & Kapodistrian University of Athens, Zografou Campus GR, Athens, 157 73, Greece
School of Science and Technology, University of Camerino, Via Madonna delle Carceri, Camerino, 62032, Italy
Department of Nanoscale Science and Engineering, University at Albany-SUNY, Albany, 12222, NY, United States
INAF - Osservatorio Astronomico di Brera, Milano, Italy
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Perugia, Perugia, 06123, Italy
Al-Farabi Kazakh National University, Al-Farabi av. 71, Almaty, 050040, Kazakhstan
Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta, Chile
Department of Mathematics, Faculty of Applied Sciences, Durban University of Technology, Durban, 4000, South Africa
School for Data Science and Computational Thinking, Department of Mathematical Sciences, Stellenbosch University, Stellenbosch, 7602, South Africa
Department of Physics
School of Science and Technology
Department of Nanoscale Science and Engineering
INAF - Osservatorio Astronomico di Brera
Istituto Nazionale di Fisica Nucleare (INFN)
Al-Farabi Kazakh National University
Departamento de Matemáticas
Department of Mathematics
School for Data Science and Computational Thinking
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