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(phi), then this potential c an be unambiguously determined from the following observational data: eithe r from the behavior of density perturbations in dustlike matter component a s a function of redshift (given the Hubble constant additionally), or from the luminosity distance as a function of redshift (given the present densit y of dustlike matter in terms of the critical value). (C) 1998 American Ins titute of Physics. [S0021-3640(98)00122-4].