Holographic Ricci–Gauss–Bonnet Dark Energy with Observational Constraints

Our study focuses on the holographic dark energy (HDE) model where the Gauss–Bonnet and Ricci invariants jointly determine the infrared cutoff. We determine which possibilities are physically plausible by examining how well the model fits the data. We challenge the cosmological model using two cosmological datasets: the Pantheon sample of Supernovae (SNIa), in conjunction with the most recent cosmic chronometer dataset, by performing Monte Carlo Markov Chain (MCMC) analyses to constrains the model parameters. The evolution of the equation of state (EoS) parameter, the deceleration parameter (DP), and the energy density parameters are thoroughly examined based on the best fit values of the model parameters. These show the typical thermal history of the universe, including the epochs of matter, radiation, and dark energy, culminating in the eventual total dominance of dark energy (DE). During the cosmological evolution, the corresponding DE EoS parameter may experience phantom divide crossing, lie in the quintessence and phantom regimes, and have an asymptotic value that is exactly equal to the cosmological-constant value. These observational datasets show a good agreement between the model and observations. The dynamical behavior of the DP explains the transition of the Gauss–Bonnet universe from decelerated to accelerated expansion. Our tools include the ( $$\omega_{D},\omega_{D}^{{}^{\prime}}$$ ) pair, and $$Om(z)$$ diagnostic planes. Our results show that, across a range of model parameter values, the model displays both Chaplygin gas and quintessence behaviors in the ( $$\omega_{D},\omega^{\prime}_{D}$$ ) planes. To set our model apart from existing DE models, we also use the $$Om(z)$$ diagnostic analysis.