Complete noncommutativity in a cosmological model with radiation

In order to try explaining the present accelerated expansion of universe, we consider most complete noncommutativity, a certain type, in Friedmann–Robertson–Walker cosmological model, coupled perfect fluid. We use ADM formalism write gravitational Hamiltonian model and Schutz’s fluid Hamiltonian. The noncommutativity is introduced by four nontrivial Poisson brackets between all geometrical as well matter variables model. Each bracket associated with noncommutative parameter. recover description terms commutative introducing transformations that depend on parameters. Using those transformations, rewrite total variables. From resulting Hamiltonian, obtain scale factor dynamical equations for generic solve these equations, restrict our attention where radiation. solutions six parameters: parameters, parameter energy C, curvature k. They also initial conditions compare corresponding ones determine how former differ from latter ones. comparison shows very useful describing universe. estimates one