Effect of the minimal length uncertainty relation on the density of states and the cosmological constant problem

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 ͔ϭiប͓(1ϩ␤ p 2 )␦ i j ϩ␤Јp i p j ͔. We point out that this relation, which is an example of a 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.

Thermodynamics of black holes in the deformed Hořava–Lifshitz gravity

“…However, it was known that the generalized uncertainty principle provides naturally a UV cutoff to the local quantum field theory as gravity effects [32,33]. The GUP relation of Eq.…”

Influence of a minimal length on the creation of scalar particles

“…This explains why various physical problems are reconsidered by taking into account the minimal length. As example, we cite the harmonic oscillator [24][25][26], the Hydrogen atom [26][27][28][29][30][31][32], the inverse square potential [33], the Dirac oscillator [34], and the resonant scattering by a potential barrier [35,36]. Elsewhere, the influence of the minimal length on the Casimir effect has been communicated in several works [37,38].…”

Hydrogen atom in momentum space with a minimal length

“…[4][5][6][7][8][9][10][11][12][13]. The idea of modifying the standard Heisenberg uncertainty relation in such a way that it includes a minimal length has first been proposed in the context of quantum gravity and string theory [14,15].…”