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Register a new userEddingtons Gravity in Immersed Spacetime
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Hemza Azri
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We formulate Eddingtons affine gravity in a spacetime which is immersed in a larger eight dimensional space endowed with a hypercomplex structure. The dynamical equation of the first immersed Ricci-type tensor leads to gravitational field equations which include matter. We also study the dynamical effects of the second Ricci-type tensor when added to the Lagrangian density. A simple Lagrangian density constructed from combination of the standard Ricci tensor and a new tensor field that appears due to the immersion, leads to gravitational equations in which the vacuum energy gravitates with a different cosmological strength as in Phys. Rev. D {bf 90}, 064017 (2014), rather than with Newtons constant. As a result, the tiny observed curvature is reproduced due to large hierarchies rather than fine-tuning.
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