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New Approach to Unimodular Relativity

S. C. Tiwari
Dec 2022
摘要
A thorough study and analysis on the conceptual foundations of unimodulargravity shows that this theory is essentially general relativity disguised asunimodular relativity in the literature. The main reason for this dilemma isaccepting the Einsteinian paradigm: general relativistic framework, covariantdivergence law for matter energy-momentum tensor, and cosmological constant asan integration constant, but introducing the artefact of unimodular descriptionabsent in Einstein's work. A new approach is proposed in this paper in whichpure unimodular relativity is defined in terms of equi-projective geodesicswith the fundamental metric tensor having determinant unity and the geometrictensors constructed from them. Modification of covariant divergence law for thematter energy-momentum tensor is shown to have two new consequences. In theconventional unimodular gravity an effective cosmological term comprising oftwo variable scalar fields, namely, the unimodular geometric ambiguity andunimodular matter energy ambiguity, is proposed. A radical departure on thecosmological constant problem is possible assuming differing evolution of thetwo scalars: the Einstein equation emerges when the two ambiguities cancel eachother. Secondly, in the case of pure unimodular relativity a gravitationalfield equation is proposed consistent with the unimodular space-time structure.
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