Necessity of Generalised Energy Conservation for de Sitter Vacua

Establish whether Generalised Energy Conservation, defined by the vanishing of non-energy-conserving de Sitter scattering amplitudes, is a necessary criterion for de Sitter vacua in quantum gravity.

Background

Generalised Energy Conservation (GEC) requires de Sitter scattering amplitudes in extended Poincaré de Sitter spacetime to vanish away from the energy-conserving locus. The paper relates violations of GEC to conformal anomalies and beta-function contributions in holographic correlators for tree-level contact interactions.

A non-energy-conserving amplitude produces a term associated with eternal energy creation or annihilation. Because such a term can generate a phase-space ultraviolet divergence and suggest vacuum instability, the paper proposes that the absence of these terms may be required in consistent de Sitter vacua, including vacua arising in quantum gravity. The necessity of this condition is stated as a conjecture rather than established generally.

References

The presence of a $\theta(-k_T)$ term signals eternal energy creation. When integrated over phase space, this term produces a UV divergence, suggesting a possible vacuum instability. We therefore conjecture that GEC is a necessary criterion for dS vacua in quantum gravity , in agreement with dS/CFT examples , as explained below.

— Conformal Anomalies and Generalised Energy Conservation in De Sitter Spacetime  (2610.08113 - Du, 6 Oct 2026) in Section 1, Generalised energy conservation and holographic consistency