How to determine an effective potential for a variable cosmological term

Abstract

It is shown that if a variable cosmological term in the present Universe is described by a scalar field with minimal coupling to gravity and with some phenomenological self-interaction potential V(ϕ), then this potential can be unambiguously determined from the following observational data: either from the behavior of density perturbations in dustlike matter component as a function of redshift (given the Hubble constant additionally), or from the luminosity distance as a function of redshift (given the present density of dustlike matter in terms of the critical value).