Can thick braneworlds be self-consistent?
  We discuss the backreaction of a massless, minimally coupled, quantized scalar field on a thick, two-dimensional de Sitter (dS) brane as an extension of our previous work. We show that a finite brane thickness naturally regularizes the backreaction on the brane. The quantum backreaction exhibits a quadratic divergence in the thin wall limit. We also give a theoretical bound on the brane thickness, in terms of the brane self-consistency of the quantum corrected Einstein equation, namely the requirement that the size of the backreaction should be smaller than that of the background stress-energy at the center of the brane. Finally, we discuss the brane self-consistency for the case of a four-dimensional dS brane. 
Masato Minamitsuji, Wade Naylor, Misao Sasaki