2015/08/31 by Piyabut Burikham, Krai Cheamsawat, Tiberiu Harko +1 · 23 citations
Physics and Astronomy · #Barotropic fluid #Black Holes and Theoretical Physics #Classical mechanics #Cosmological constant #Cosmology #Cosmology and Gravitation Theories #Dark energy #De Sitter space #De Sitter universe #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Universe #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1140/epjc/s10052-015-3673-5
published in The European Physical Journal C 75(9) (Springer Science+Business Media) · 16 pages, one figure; Section IV extended; references added; accepted for publication in EPJC
openalex publication_date 2015/09/01 · arxiv created 2015/09/07 · arxiv updated 2015/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The existence of both a minimum mass and a minimum density in nature, in the presence of a positive cosmological constant, is one of the most intriguing results in classical general relativity. These results follow rigorously from the Buchdahl inequalities in four-dimensional de Sitter space. In this work, we obtain the generalized Buchdahl inequalities in arbitrary space–time dimensions with Λ ≠ 0 and consider both the de Sitter and the anti-de Sitter cases. The dependence on D, the number of space–time dimensions, of the minimum and maximum masses for stable spherical objects is explicitly obtained. The analysis is then extended to the case of dark energy satisfying an arbitrary linear barotropic equation of state. The Jeans instability of barotropic dark energy is also investigated, for arbitrary D, in the framework of a simple Newtonian model with and without viscous dissipation, and we determine the dispersion relation describing the dark energy–matter condensation process, along with estimates of the corresponding Jeans mass (and radius). Finally, the quantum mechanical implications of the mass limits are investigated, and we show that the existence of a minimum mass scale naturally leads to a model in which dark energy is composed of a ‘sea’ of quantum particles, each with an effective mass proportional to Λ 1/4 .