The Effect of the Minimal Length Uncertainty Relation on the Density of States and the Cosmological Constant Problem

TL;DR

This paper explores how a minimal length uncertainty relation, inspired by string theory, affects the density of states and suggests a potential link to the cosmological constant problem, though the observable effects are minimal.

Contribution

It demonstrates that the minimal length uncertainty relation can imply a finite cosmological constant and discusses its implications for blackbody radiation spectra.

Findings

The minimal length relation leads to a finite cosmological constant.

Blackbody spectrum modifications are too small to detect in CMB.

Provides insight into UV/IR correspondence and cosmological constant.

Abstract

We investigate the effect of the minimal length uncertainty relation, motivated by perturbative string theory, on the density of states in momentum space. The relation is implemented through the modified commutation relation [x_i,p_j]=i hbar[(1 + beta p^2) delta_{ij} + beta' p_i p_j]. We point out that this relation, which is an example of an UV/IR relation, implies the finiteness of the cosmological constant. While our result does not solve the cosmological constant problem, it does shed new light on the relation between this outstanding problem and UV/IR correspondence. We also point out that the blackbody radiation spectrum will be modified at higher frequencies, but the effect is too small to be observed in the cosmic microwave background spectrum.