Semiclassical Cosmological Constant in Anti-de Sitter and de Sitter Spacetimes
Abstract
We investigate the semiclassical Einstein equation for a quantized scalar field in four-dimensional anti-de Sitter (AdS) and de Sitter (dS) spacetimes. We first determine self-consistent configurations by fixing the bare cosmological constant to its geometric value, requiring the renormalized vacuum stress-energy tensor to vanish. In AdS, the resulting mass-curvature relations depend on the curvature coupling and boundary conditions; one formal Neumann root for minimal coupling is excluded by the admissible parameter range, whereas both Dirichlet and Neumann solutions are allowed for conformal coupling. In dS, we recover the known self-consistent solution for a minimally coupled massive field. We then evaluate the effective cosmological constant on prescribed backgrounds in four massless configurations. In each case, it takes the form Λeff=A/ℓ2+B/ℓ4. The competition between classical curvature and vacuum polarization produces a minimum and a zero in the minimally coupled AdS case, while the other configurations are monotonic. Finally, the formal continuation ℓ→ iℓ fails to reproduce the directly calculated quantum coefficients: their AdS-to-dS ratios are 29/61 for minimal coupling and −1 for conformal coupling. These results show that continuation of the curvature scale alone does not establish equivalence between the semiclassical vacuum contributions in AdS and dS.
Related
- Post-Newtonian theory in de Sitter and anti-de Sitter spacetimes
- Alternative Boundary Conditions in Asymptotically Anti-de Sitter Spacetimes
- Semiclassical effects on ultramassive spacetimes
- Geometrically Induced Semiclassical Limit for Quasinormal Modes and Greybody Factors in Higher-Dimensional Near-Ultracold spacetimes
- The generalized entropy in holographic semiclassical de Sitter spacetime
BibTeX
@misc{mamanileqque2026semiclassical,
title = {{Semiclassical Cosmological Constant in Anti-de Sitter and de Sitter Spacetimes}},
author = {Milton C. Mamani-Leqque},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09436},
eprint = {2610.09436},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09436},
}
RIS
TY - UNPB
TI - Semiclassical Cosmological Constant in Anti-de Sitter and de Sitter Spacetimes
AU - Milton C. Mamani-Leqque
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.09436
UR - https://arxiv.org/abs/2610.09436
AB - We investigate the semiclassical Einstein equation for a quantized scalar field in four-dimensional anti-de Sitter (AdS) and de Sitter (dS) spacetimes. We first determine self-consistent configurations by fixing the bare cosmological constant to its geometric value, requiring the renormalized vacuum stress-energy tensor to vanish. In AdS, the resulting mass-curvature relations depend on the curvature coupling and boundary conditions; one formal Neumann root for minimal coupling is excluded by the admissible parameter range, whereas both Dirichlet and Neumann solutions are allowed for conformal coupling. In dS, we recover the known self-consistent solution for a minimally coupled massive field. We then evaluate the effective cosmological constant on prescribed backgrounds in four massless configurations. In each case, it takes the form Λ_eff=A/ℓ^2+B/ℓ^4. The competition between classical curvature and vacuum polarization produces a minimum and a zero in the minimally coupled AdS case, while the other configurations are monotonic. Finally, the formal continuation ℓ→ iℓ fails to reproduce the directly calculated quantum coefficients: their AdS-to-dS ratios are 29/61 for minimal coupling and −1 for conformal coupling. These results show that continuation of the curvature scale alone does not establish equivalence between the semiclassical vacuum contributions in AdS and dS.
ER -