Check of the Mass Bound Conjecture in the de Sitter Space

TL;DR

The paper tests the BBM conjecture, which posits that any asymptotically de Sitter space with mass $M$ exceeding that of pure de Sitter space contains a cosmological singularity, by analyzing a topological de Sitter solution and its dilatonic deformation. Using the surface counterterm method to compute the quasilocal stress-energy tensor, the authors obtain the conserved mass and demonstrate that $M > M_{\rm dS}$ in these examples, while the cosmological horizons satisfy the first law of thermodynamics $dM = T_{HK} dS$. The dilatonic deformation, though not asymptotically dS, still yields a positive mass above the vacuum and a consistent thermodynamic structure, with a nonconformal Euclidean QFT dual, extending the dS/CFT framework to a domain-wall/QFT context. Collectively, the results support the BBM conjecture and suggest a nonconformal holographic correspondence for asymptotically dS spaces with cosmological singularities, with potential implications for entropy bounds and energy conditions in such spacetimes.

Abstract

Recently an interesting conjecture was put forward which states that any asymptotically de Sitter space whose mass exceeds that of exact de Sitter space contains a cosmological singularity. In order to test this mass bound conjecture, we present two solutions. One is the topological de Sitter solution and the other is its dilatonic deformation. Although the latter is not asymptotically de Sitter space, the two solutions have a cosmological horizon and a cosmological singularity. Using surface counterterm method we compute the quasilocal stress-energy tensor of gravitational field and the mass of the two solutions. It turns out that this conjecture holds within the two examples. Also we show that the thermodynamic quantities associated with the cosmological horizon of the two solutions obey the first law of thermodynamics. Furthermore, the nonconformal extension of dS/CFT correspondence is discussed.