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Observational constraints on G-corrected holographic dark energy using a Markov chain Monte Carlo method

We constrain holographic dark energy (HDE) with time varying gravitational coupling constant in the framework of the modified Friedmann equations using cosmological data from type Ia supernovae, baryon acoustic oscillations, cosmic microwave background radiation and X-ray gas mass fraction. Applying a Markov Chain Monte Carlo (MCMC) simulation, we obtain the best fit values of the model and cosmological parameters within $1σ$ confidence level (CL) in a flat universe as: $Ω_{\rm b}h^2=0.0222^{+0.0018}_{-0.0013}$, $Ω_{\rm c}h^2 =0.1121^{+0.0110}_{-0.0079}$, $α_{\rm G}\equiv \dot{G}/(HG) =0.1647^{+0.3547}_{-0.2971}$ and the HDE constant $c=0.9322^{+0.4569}_{-0.5447}$. Using the best fit values, the equation of state of the dark component at the present time $w_{\rm d0}$ at $1σ$ CL can cross the phantom boundary $w=-1$.