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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 solutionin Euclidean space) which exists in casually connected two regions of thespacetime. The thermalon plays a major role in gravitational phase transitionby inducing the decay of the negative effective cosmological constant to thepositive one due to the higher-order gravity effects. The thermodynamics phasespace of the Hawking temperature and free energy is investigated in details. Wefind that the free energy of the thermalon is always negative at the maximum ofHawking temperature for all possible values of the Gauss-Bonnet couplings. Thismeans that the phase transition mediated by thermalon from AdS to dSasymptotics is inevitable according to the presence of the massive gravity.More importantly, the parameters of the massive gravity behave similarly to theorder parameters in the phase transition instead of the Gauss-Bonnet coupling.

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