Affine theory of gravitation
  We propose a new theory of gravitation, in which the affine connection is the
only dynamical variable describing the gravitational field. We construct the
simplest dynamical Lagrangian density that is entirely composed from the
connection, via its curvature and torsion, and is an algebraic 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,
$k_{\mu\nu}=S^\rho_{\lambda\mu}S^\lambda_{\rho\nu}$. 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
$k_{\mu\nu}$. 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 $k_{\mu\nu}$ is regarded as 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
physically valid construction of the metric as an algebraic function of the
connection, and naturally explains dark energy as an intrinsic property of
spacetime. The observed accelerating expansion of the Universe may be the
strongest evidence for torsion.
