de Sitter-holographic C functions with a topological, dilatonic twist -: art. no. 064001

Recently, the holographic aspects of asymptotically de Sitter spacetimes have generated substantial literary interest. The plot continues in this paper, as we investigate a certain class of dilatonically deformed "topological" de Sitter solutions [which were introduced by R. Cai, Y. Myung, and Y. Zhang, Phys. Rev. D 65, 084019 (2002)]. Although such solutions possess a detrimental cosmological singularity, their interpretation from a holographic perspective remains somewhat unclear. The current focus is on the associated generalized C functions, which are shown to maintain their usual monotonicity properties in spite of this exotic framework. These findings suggest that such topological solutions may still play a role in our understanding of quantum gravity with a positive cosmological constant.