Chronos said:Wiki gives a good treatise
http://en.wikipedia.org/wiki/Friedmann_equations
The Friedmann equation, named after the Russian physicist Alexander Friedmann, is a fundamental equation in cosmology that describes the expansion of the universe. It represents the relationship between the rate of expansion of the universe and the matter and energy content of the universe.
The Friedmann equation is derived from Einstein's field equations in general relativity, which describe the curvature of spacetime in the presence of matter and energy. By assuming a homogeneous and isotropic universe, the Friedmann equation can be derived as a solution to these equations.
The Friedmann equation is significant because it provides a mathematical framework for understanding the expansion of the universe. It also allows us to make predictions about the past and future evolution of the universe, and has been confirmed by numerous observations and experiments.
The Friedmann equation is used in cosmological models to determine the evolution of the universe over time. By inputting different values for the matter and energy content of the universe, we can create different models that can help us understand the structure and dynamics of the universe.
Yes, there are limitations to the Friedmann equation. It assumes a homogeneous and isotropic universe, which may not be true on small scales. It also does not account for the effects of dark energy, which is believed to be responsible for the accelerated expansion of the universe. Additionally, the equation does not take into account the effects of other fundamental forces, such as gravity and electromagnetism.