HIGHER DIMENSIONAL DUST COSMOLOGICAL IMPLICATIONS OF A DECAY LAW FOR THE Λ TERM: EXPRESSIONS FOR SOME OBSERVABLE QUANTITIES

Abstract

We have considered the multidimensional cosmological implications of a decay law for the Λ term that is proportional to [Formula: see text], where β is a constant and a is the scale factor of RW-space–time. We discuss the cosmological consequences of a model for the vanishing pressure for the case k = 0. It has been observed that such models are compatible with the result of recent observations and the cosmological term Λ gradually reduces as the universe expands. In this model, Λ varies as the inverse square of time, which matches its natural units. The proper distance, the luminosity distance-redshift, the angular diameter distance-redshift, and look back time-redshift for the model are presented in the framework of higher dimensional space–time. The model of the Freese et al. (Nucl. Phys. B287, 797 (1987)) for n = 2 is retrieved for the particular choice of A0and also the Einstein–de Sitter model is obtained for [Formula: see text]. This work has thus generalized to higher dimensions the well-known result in four-dimensional space–time. It is found that there may be a significant difference, in principle at least, to the analogous situation in four-dimensional space–time.