  In the de Sitter gauge theory (DGT), the fundamental variables are the de
Sitter (dS) connection and the gravitational Higgs/Goldstone field $\xi^A$.
Previously, a model for DGT was analyzed, which generalizes the
MacDowell--Mansouri gravity to have a variable cosmological constant
$\Lambda=3/l^2$, where $l$ is related to $\xi^A$ by $\xi^A\xi_A=l^2$. It was
shown that the model sourced by a perfect fluid does not support a radiation
epoch and the accelerated expansion of the parity invariant universe. In this
work, I consider a similar model, namely, the Stelle--West gravity, and couple
it to a modified perfect fluid, such that the total Lagrangian 4-form is
polynomial in the gravitational variables. The Lagrangian of the modified fluid
has a nontrivial variational derivative with respect to $l$, and as a result,
the problems encountered in the previous work no longer appear. Moreover, to
explore the elegance of the general theory, as well as to write down the basic
framework, I perform the Lagrange--Noether analysis for DGT sourced by a matter
field, yielding the field equations and the identities with respect to the
symmetries of the system. The resulted formula are dS covariant and do not rely
on the existence of the metric field.
