In this paper, we study the cosmological constant emerging from the Wheeler-DeWitt equation as an eigenvalue of the related Sturm-Liouville problem. We employ Gaussian trial functionals and we perform a mode decomposition to extract the transverse-traceless component, namely, the graviton contribution, at one loop. We implement a noncommutative-geometry-induced minimal length to calculate the number of graviton modes. As a result, we find regular graviton fluctuation energies for the Schwarzschild, de Sitter, and anti-de Sitter backgrounds. No renormalization scheme is necessary to remove infinities, in contrast to what happens in conventional approaches.
|Original language||English (US)|
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|State||Published - Mar 15 2011|
ASJC Scopus subject areas
- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)