Eddington's Gravity in Immersed Spacetime
arXiv:1501.06177 · doi:10.1088/0264-9381/32/6/065009
Abstract
We formulate Eddington's 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 Newton's constant. As a result, the tiny observed curvature is reproduced due to large hierarchies rather than fine-tuning.
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- Separate Einstein-Eddington Spaces and the Cosmological Constant
- Ricci-Determinant Gravity: Dynamical Aspects and Astrophysical Implications
- Dynamical aspects of asymmetric Eddington gravity with scalar fields
- Affine Dynamics with Torsion