A non-anthropic origin for a small cosmological constant

An impressive variety of recent observations which include luminosity evolu tions of high redshift supernovae strongly suggest that the cosmological co nstant (Lambda) is not zero. Even though the Lambda-term may dominate cosmi c dynamics at the present epoch, such a value for the vacuum energy is actu ally unnaturally small. The difficulties in finding a suitable explanation (based on fundamental physics) for such a small residual value for the cosm ological term has led several authors to resort to an anthropic explanation for its existence. Here we present a few examples which invoke phase trans itions in the early universe involving strong or electroweak interactions t o show how the cosmical term of the correct observed magnitude can arise fr om fundamental physics involving gravity.