  We present a simplicial model for gravity written in terms of a discretized
Lorentz connection and a discretized tetrad field. The continuum limit of its
action is Holst's action for general relativity. With the intention of using it
to construct spin foam modes for quantum gravity, we write two other equivalent
models written in terms of a discretized and constrained $B$ field. The
differences between our model and existing models are most likely inessential
in the sense that a quantization would lead to equivalent quantum theories in
the Wilsonian continuum limit. Nevertheless, we mention two features leading to
possible advantages: Curvature degrees of freedom are described at the level of
each 4-simplex. Our model offers a picture of bulk geometry leading to actions
for matter couplings that split as a sum over 4-simplices.

General Relativity and Quantum Cosmology