  The Hamiltonian formalism of Einstein--Cartan (EC) gravity is a starting
point for canonical quantum gravity. The existing formalisms are at most
Lorentz covariant, or diffeomorphism covariant. Here we analyze the Hamiltonian
EC gravity in a 5d covariant way, with the gauge group being the de Sitter (dS)
group, which unifies the Lorentz transformations and translation in an elegant
manner, and also coincides with the acceleration of the universe. We
reformulate the EC equations into a dS-covariant form, then find out the
dS-covariant constraints of the phase space, and make all the constraint
functions constitute a closed algebra by constructing a dS-invariant Dirac
bracket, for the purpose of quantization.
