Locally Localized Gravity and Geometric Transitions

Abstract

In this paper we analyze the local localization of gravity in $Ad{S}_4$ thick brane embedded in $Ad{S}_5$ 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 $T_{\ast },$ where the thick 3-brane engenders the geometric $AdS/M/dS$ transitions.

Comments: Latex, 16 pages, 8 eps figures, 1 table