Abstract
The steps followed by Einstein when he first wrote on cosmology from the point of view of the general theory of relativity are revised. It is argued that his insightful line of thought leading to the introduction of the cosmological constant in the equations of motion has only one weakness: the constancy of the cosmological term, or what is the same, its independence of the matter content of the universe. Eliminating this feature, a simple and reasonable modification of the cosmological equations of motion is proposed. The solutions of the new cosmological equations give rise to a cosmological model that tries to approach the Einstein static solution. This model exhibits very appealing features in terms of fitting current observations.
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