Cosmological Constant in a Regge State-Sum Model of Quantum Gravity Aleksandar MIKOVI ´ C 1,2 and Marko VOJINOVI ´ C 2 1 Departamento de Matem´atica Universidade Lus´ofona de Humanidades e Tecnologias Av. do Campo Grande, 376, 1749-024 Lisboa, Portugal 2 Grupo de Fisica Matem´atica da Universidade de Lisboa Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal E-mail: amikovic@ulusofona.pt, vmarko@ipb.ac.rs Abstract We study the quantum contributions to the classical cosmological con- stant in a Regge state-sum model of quantum gravity by using the effective action approach. We use a special path-integral (PI) measure which depends on a free parameter and we include matter, in the form of a massive scalar field. The effective cosmological constant (CC) is given as a sum of 3 terms: the classical CC, the quantum gravity CC and the matter CC. Since one can measure only the sum of these 3 terms, we show that the matter CC can be cancelled by the classical CC so that the effective CC is given by the quantum gravity CC. Since the value of the quantum gravity CC is determined by the PI measure only, the PI measure parameter can be chosen such that the effective CC gives the observed value. 1. Introduction The cosmological constant problem, for a review see [1], is the problem of explaining the presently observed value of the cosmological constant (CC) within a quantum theory of matter and gravitation. In any quantum gravity (QG) theory there should be a natural length scale, which is the Planck length l P ≈ 10 -35 m. Consequently, the quantum correction to the classical value of CC should be of order l -2 P . However, this natural theoretical value is 10 122 times larger from the observed value [2], and the problem is to explain 1 arXiv:1407.1124v5 [gr-qc] 9 Jan 2015