Affine theory of gravitation

作者：Poplawski Nikodem^*

来源：General Relativity and Gravitation, 2014, 46(1): 1625.

DOI：10.1007/s10714-013-1625-7

• Affine connection
• Torsion tensor
• Cosmological constant
• Dark energy

We propose a theory of gravitation, in which the affine connection is the only dynamical variable describing the gravitational field. We construct a simple dynamical Lagrangian density that is entirely composed from the connection, via its curvature and torsion, and is a polynomial function of its derivatives. It is given by the contraction of the Ricci tensor with a tensor which is inverse to the symmetric, contracted square of the torsion tensor, k(mu upsilon). = (S lambda mu S rho upsilon lambda)-S-rho. We vary the total action for the gravitational field and matter with respect to the affine connection, assuming that the matter fields couple to the connection only through k(mu upsilon). We derive the resulting field equations and show that they are identical with the Einstein equations of general relativity with a nonzero cosmological constant if the tensor (mu upsilon). is regarded as proportional to the metric tensor. The cosmological constant is simply a constant of proportionality between the two tensors, which together with c and G provides a natural system of units in gravitational physics. This theory therefore provides a physical construction of the metric as a polynomial function of the connection, and explains dark energy as an intrinsic property of spacetime.

• 出版日期2014-1