dS-Holographic C-Functions with a Topological, Dilatonic Twist

TL;DR

This paper explores topologically deformed de Sitter solutions with dilaton fields, demonstrating that their associated generalized C-functions remain monotonic despite cosmological singularities, thus offering insights into holography and quantum gravity with a positive cosmological constant.

Contribution

It introduces and analyzes a class of dilatonically deformed topological de Sitter solutions, showing their C-functions preserve monotonicity, which was previously uncertain in such frameworks.

Findings

C-functions remain monotonic despite singularities

Topological solutions may inform quantum gravity with positive cosmological constant

Holographic properties extend to dilatonically deformed de Sitter spaces

Abstract

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 in hep-th/0110234). 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.