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Thermalon mediated AdS to dS phase transitions in Einstein-Gauss-Bonnet-massive gravity

In this work, gravitational phase transition emerging from anti de-Sitter (AdS) to de-Sitter (dS) vacua in Einstein-Gauss-Bonnet-massive gravity (EGBMG) is considered. We determine the location of thermalon (a static bubble solution in Euclidean space) which exists in casually connected two regions of the spacetime. The thermalon plays a major role in gravitational phase transition by inducing the decay of the negative effective cosmological constant to the positive one due to the higher-order gravity effects. The thermodynamics phase space of the Hawking temperature and free energy is investigated in details. We find that the free energy of the thermalon is always negative at the maximum of Hawking temperature for all possible values of the Gauss-Bonnet couplings. This means that the phase transition mediated by thermalon from AdS to dS asymptotics is inevitable according to the presence of the massive gravity. More importantly, the parameters of the massive gravity behave similarly to the order parameters in the phase transition instead of the Gauss-Bonnet coupling.