An impressive variety of recent observations which include luminosity evolutions of high redshift supernovae strongly suggest that the cosmological constant (#LAMBDA#) is not zero. Even though the #LAMBDA#-term may dominate cosmic dynamics at the present epoch, such a value for the vacuum energy is actually unnaturally small. The difficulties in finding a suitable explanation (based on fundamental physics) for such a small residual value for the cosmological term has led several authors to resort to an anthropic explanation for its existence. Here we present a few examples which invoke phase transitions in the early universe involving strong or electroweak interactions to show how the cosmical term of the correct observed magnitude can arise from fundamental physics involving gravity.
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