Resolving the Cosmological Constant Problem: Black Hole Entropy and Finite Geometry

The cosmological constant problem remains one of the most profound mysteries in physics. By dimensional analysis and effective field theory, Λ, the cosmological constant, is expected to be of the order m_P^2. Accordingly, the product of Λ and the Planck length squared must be nearly 1. By contrast, cosmological observations show that this product is close to the square of the ratio of the Planck length to the Hubble length l_H, meaning that Λ is of the order l_H^(-2). Thus, the cosmological constant problem can be framed as the question of how l_H gets involved in the prediction for Λ. The present paper demonstrates that such an involvement is a result of a straightforward combination of the black hole entropy bound with the assumption of a finite number of hodons, the fundamental elements of physical space.