(Submitted on 1 Mar
2012)

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 the
observed dark energy as an intrinsic property of spacetime.

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