How to determine an effective potential for a variable cosmological term

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). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 721–726 (25 November 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.