https://doi.org/10.1140/epjc/s10052-025-14796-5
Regular Article - Theoretical Physics
CDM-like evolution in Einstein-scalar-Gauss–Bonnet gravity
1
Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016, Lisbon, Portugal
2
Departamento de Física, Faculdade de Ciências da Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016, Lisbon, Portugal
3
Departamento de Física Teórica, Universidad Complutense de Madrid, 28040, Madrid, Spain
4
Institute of Physics, W. Ostwaldi 1, 50411, Tartu, Estonia
Received:
3
June
2025
Accepted:
14
September
2025
Published online:
21
September
2025
In this work, we analyze the Einstein-scalar-Gauss–Bonnet (EsGB) theory of gravity in a cosmological context using the formalism of dynamical systems. We obtain the equations of motion of the theory and introduce an appropriate set of dynamical variables to allow for a direct comparison with the results from General Relativity (GR). We observe that the cosmological phase space features the same set of fixed points as in standard GR, i.e., radiation-dominated, matter-dominated, curvature-dominated, and exponentially-accelerated solutions independently of the values of the coupling function and the scalar field. Furthermore, the radiation-dominated fixed points are repellers and the exponentially accelerated fixed points are attractors in the phase space, thus allowing for cosmological solutions behaving qualitatively similar to the CDM model, i.e., transitioning from a radiation-dominated phase into a matter-dominated phase, and later into a late-time cosmic acceleration phase supported by the scalar field potential. Following a reconstruction method through which we produce the cosmological solutions in the GR limit of the theory and introduce them into the general EsGB dynamical system, a numerical integration of the dynamical system shows that the EsGB theory provides cosmological solutions indistinguishable from those of the standard CDM model, compatible with the current observations from the Planck satellite and weak-field solar system dynamics, while maintaining the scalar field and the coupling function finite and regular throughout the entire time evolution.
© The Author(s) 2025
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