A theoretical model of anti-de Sitter cosmology reports two sharply different outcomes in selected calculations. At lambda = 100, the model's expansion-rate measure stays positive while curvature approaches zero; at lambda = 103, the expansion-rate measure remains negative, heads toward minus infinity and the modeled universe reaches a singularity.
The contrast is not presented as one universal response to negative vacuum energy. The trajectories come from selected parameter scenarios for a scalar field coupled to curvature, and the paper reports a threshold beyond which compensation fails when beta = -1.
A calculation built around a stripped-down universe
The work is an arXiv version 1 preprint. Its central question is whether a scalar-field mechanism can compensate the gravitational effect of initially large negative vacuum energy and avert anti-de Sitter collapse. The authors evaluate that question through numerical and analytical calculations.
The baseline is a pure anti-de Sitter universe containing only negative vacuum energy and no matter. For that setup, the model chooses sigma = 1, beta = -1 and a massless scalar field with m = 0.
The cosmological evolution is solved numerically from the coupled equations under selected coupling parameters, with curvature represented by r. The analysis also examines the late-time equations analytically so that the reported asymptotic forms can be compared with the numerical trajectories.
The reported paths differ at different parameters
For lambda = 100, the reported trajectory stabilizes with a positive, decreasing Hubble parameter, scaling roughly as 1/tau. Its curvature asymptotically approaches zero. In ordinary terms, the model continues expanding while its expansion rate falls.
At lambda = 103, the scalar field is described as too weak. Curvature and the Hubble parameter remain negative, H tends to minus infinity, and the modeled universe reaches a singularity.
The paper describes a critical vacuum-energy threshold, written as the absolute value of lambda crit. With beta = -1, it says compensation fails when the initial negative vacuum energy exceeds that threshold. The supplied analysis does not report a numerical value for the threshold or an uncertainty estimate for these selected calculations.
A separate parameter case also avoids collapse
A separate calculation uses lambda = 104 and beta = -10. In that reported trajectory, curvature approaches zero, the modeled singularity is avoided, and the evolution changes from anti-de Sitter behavior to power-law expansion.
This is a selected parameter case, not an isolated test of the coupling strength. Both lambda and beta differ from the earlier reported examples, so the comparison does not isolate beta as the sole changing parameter.
The late-time picture
To describe the late-time regime, the authors set r = 0 and solve the asymptotic equations analytically. They report limiting forms for h, the scalar-field derivative phi-prime and the scalar field phi, and say those forms match the numerical calculations.
The paper identifies the corresponding Hubble behavior with the canonical expansion law of a radiation-dominated cosmology. This is a model-derived late-time power-law description, not an observational validation.
An interpretation, not an observation
The authors' interpretation is that physical vacuum energy remains present while its gravitational impact is neutralized by the scalar-curvature interaction. The proposed compensation therefore concerns the way the vacuum energy enters the modeled gravitational dynamics, not removal of the energy itself.
Where the model stops
The geometry is deliberately narrow. The FLRW analysis assumes flat three-dimensional space, which the authors describe as a simplifying assumption for studying the mechanism. The reported trajectories stay within that flat setup.
The supplied analysis reports no empirical validation and no uncertainty estimates for the selected numerical and analytical scenarios. It also does not present a systematic parameter scan, so the reported paths should be read as modeled behavior under stated assumptions rather than a result for every negative vacuum energy.
The baseline contains no matter, and the authors list inclusion of non-relativistic matter and a test of transition to matter-dominated cosmology as next steps. They also leave a dark-energy extension involving more complicated curvature dependence for future work.
The work remains a preprint
The front matter identifies the paper as an arXiv version 1 preprint and shows the dates August 27, 2026, and 26 Aug 2026. Its evidence remains the selected model solutions described above.
The work was supported by state funding for neutrino physics, FSUS-2025-0019.
Paper data and sources
Original title: Vacuum energy problem in anti-de Sitter space
Authors: E. V. Arbuzova, A. D. Dolgov
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text