Researchers have formulated a six-field Rational Extended Thermodynamics (RET$_6$) model for relativistic polyatomic gases in curved spacetime. This model, based on a polyatomic extension of the Boltzmann-Chernikov kinetic equation, incorporates dynamical pressure as the sole non-equilibrium variable. The one-particle distribution in this framework also depends on an internal-energy variable, and the closure of the associated relativistic moment hierarchy is achieved via the Maximum Entropy principle. The field equations, closure relations, and production term are directly derived from the underlying kinetic structure, rather than being phenomenologically postulated.

The RET$_6$ model is extended from Minkowski spacetime to a general curved spacetime through minimal coupling and linked to Einstein's equations. A key structural result is a kinetic-theory no-go theorem stating that any stress-energy tensor induced by a non-negative relativistic one-particle distribution function satisfies the strong energy condition. When applied to a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime, it is observed that dynamical pressure modifies the expansion compared to the perfect-fluid Euler case, although the no-go theorem precludes acceleration driven solely by the RET$_6$ gas.

Finally, by reintroducing a cosmological constant, the combined $\Lambda$RET$_6$ model demonstrates the existence and local stability of a de Sitter attractor at late times. Numerical simulations indicate that, for physically motivated post-recombination initial data and relaxation times, the expansion history rapidly approaches that of the $\Lambda$CDM model. The small non-equilibrium corrections observed are controlled by the relaxation time and the initial value of the dynamical pressure, suggesting this model may offer a more complete description of cosmological dynamics in certain phases.