Lastly, the inverse Lagrangian problem has been tackled through an analogy with the Friedmann equation from cosmology, suggesting new Lagrangian and Hamiltonian formulations for Riccati equations.

This model, they argue, shows that “a simple expansion law consistent with Einstein’s general relativity does not have to obey Friedmann’s equation.” To clarify how these two models differ ...

These frameworks modify the classical Poisson algebra to explore how they can account for the modified Friedmann equations that arise in loop quantum cosmology. The findings suggest that while ...