2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184531In this paper we analyze the local localization of gravity in $AdS_4$ thick brane embedded in $AdS_5$ space. The 3-brane is modelled by domain wall solution of a theory with a bulk scalar field coupled to five-dimensional gravity. In addition to small four-dimensional cosmological constant, the vacuum expectation value (vev) of the scalar field controls the emergence of a localized four-dimensional quasi-zero mode. We introduce high temperature effects, and we show that gravity localization on a thick 3-brane is favored below a critical temperature $T_c$. These investigations suggest the appearance of another critical temperature $T_*,$ where the thick 3-brane engenders the geometric $AdS/M/dS$ transitions.Latex, 16 pages, 8 eps figures, 1 tableHigh Energy Physics - TheoryGeneral Relativity and Quantum CosmologyHigh Energy Physics - Phenomenologytext