Implications of a cosmological constant varying as<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">−</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>

We advocate the possibility that the (effective) cosmological constant \ensuremath{\Lambda} varies in time as ${R}^{\mathrm{\ensuremath{-}}2}$, R being the scale factor of our expanding Universe. This behavior can be obtained under some simple and general assumptions in conformity with quantum cosmology. After pointing out several advantages worth noticing, we show that such a time-varying \ensuremath{\Lambda} leads to no conflict with existing observations. However, it does change the predictions of the standard cosmology in the matter-dominated epoch and alleviates some problems in reconciling observations with the inflationary scenario. In particular, this ``medium'' time variation of \ensuremath{\Lambda} leads to creation of matter with a rate at present which is comparable to that in the steady-state cosmology.

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