Quintessence in the Weyl-Gauss-Bonnet Model

José Jaime Terente Díaz, Konstantinos Dimopoulos, Mindaugas Karčiauskas, Antonio Racioppi
General Relativity and Quantum Cosmology, General Relativity and Quantum Cosmology (gr-qc), Cosmology and Nongalactic Astrophysics (astro-ph.CO), High Energy Physics - Phenomenology (hep-ph)
2023-10-11 16:00:00
Quintessence models have been widely examined in the context of scalar-Gauss-Bonnet gravity, a subclass of Horndeski's theory, and were proposed as viable candidates for Dark Energy. However, the relatively recent observational constraints on the speed of gravitational waves $c_{\textrm{GW}}$ have resulted in many of those models being ruled out because they predict $c_{\textrm{GW}} \neq c$ generally. While these were formulated in the metric formalism of gravity, it was found later that some Horndeski models could be rescued in the Palatini formalism, where the connection is independent of the metric and the underlying geometry no longer corresponds to the pseudo-Riemannian one. Motivated by this and the relation between scalar-Gauss-Bonnet gravity and Horndeski's theory, we put forward a new quintessence model with the scalar-Gauss-Bonnet action but in Weyl geometry. We find the fixed points of the dynamical system under some assumptions and determine their stability via linear analysis. Although the past evolution of the Universe as we know it is correctly reproduced, the constraints on $c_{\textrm{GW}}$ are shown to be grossly violated for the coupling function under consideration. The case of $c_{\textrm{GW}} = c$ is regarded also, but no evolution consistent with other cosmological observations is obtained.
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