A noncommutative approach to the cosmological constant problem

TL;DR

This paper investigates the cosmological constant via a noncommutative geometric approach, analyzing graviton contributions at one loop without renormalization, across various spacetime backgrounds.

Contribution

It introduces a noncommutative-geometry-based minimal length to compute graviton modes, avoiding traditional renormalization procedures.

Findings

Regular graviton fluctuation energies obtained for different backgrounds

No need for renormalization to handle infinities

Demonstrates a noncommutative approach to quantum gravity issues

Abstract

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.