Milton C. Mamani-Leqque

arXiv2026

Semiclassical Cosmological Constant in Anti-de Sitter and de Sitter Spacetimes

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 $Λ_{\mathrm{eff}}=A/\ell^2+B/\ell^4$. 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 $\ell\rightarrow i\ell$ 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.

gr-qc↗

arXiv2025

Renormalisation in maximally symmetric spaces and semiclassical gravity in Anti-de Sitter spacetime

We obtain semiclassical gravity solutions in the Poincaré fundamental domain of $(3+1)$-dimensional Anti-de Sitter spacetime, PAdS$_4$, with a (massive or massless) Klein-Gordon field (with possibly non-trivial curvature coupling) with Dirichlet or Neumann boundary. Some results are explicitly and graphically presented for special values of the mass and curvature coupling (e.g. minimal or conformal coupling). In order to achieve this, we study in some generality how to perform the Hadamard renormalisation procedure for non-linear observables in maximally symmetric spacetimes in arbitrary dimensions, with emphasis on the stress-energy tensor. We show that, in this maximally symmetric setting, the Hadamard bi-distribution is invariant under the isometries of the spacetime, and can be seen as a `single-argument' distribution depending only on the geodesic distance, which significantly simplifies the Hadamard recursion relations and renormalisation computations.

gr-qc↗